diff --git a/docs/pages/api-docs/data-grid/data-grid-pro.json b/docs/pages/api-docs/data-grid/data-grid-pro.json
index ebdbd56250275..12bd2de04e4ba 100644
--- a/docs/pages/api-docs/data-grid/data-grid-pro.json
+++ b/docs/pages/api-docs/data-grid/data-grid-pro.json
@@ -312,6 +312,7 @@
       "columnHeaderDropZone",
       "columnHeaderTitle",
       "columnHeaderTitleContainer",
+      "columnHeaderTitleContainerContent",
       "columnHeaders",
       "columnHeadersInner",
       "columnHeadersInner--scrollable",
diff --git a/docs/pages/api-docs/data-grid/data-grid.json b/docs/pages/api-docs/data-grid/data-grid.json
index 26992b12e18f6..91db2cefd626a 100644
--- a/docs/pages/api-docs/data-grid/data-grid.json
+++ b/docs/pages/api-docs/data-grid/data-grid.json
@@ -259,6 +259,7 @@
       "columnHeaderDropZone",
       "columnHeaderTitle",
       "columnHeaderTitleContainer",
+      "columnHeaderTitleContainerContent",
       "columnHeaders",
       "columnHeadersInner",
       "columnHeadersInner--scrollable",
diff --git a/docs/pages/x/api/data-grid/data-grid-pro.json b/docs/pages/x/api/data-grid/data-grid-pro.json
index bf98f6da8b08e..175fe126a6563 100644
--- a/docs/pages/x/api/data-grid/data-grid-pro.json
+++ b/docs/pages/x/api/data-grid/data-grid-pro.json
@@ -312,6 +312,7 @@
       "columnHeaderDropZone",
       "columnHeaderTitle",
       "columnHeaderTitleContainer",
+      "columnHeaderTitleContainerContent",
       "columnHeaders",
       "columnHeadersInner",
       "columnHeadersInner--scrollable",
diff --git a/docs/pages/x/api/data-grid/data-grid.json b/docs/pages/x/api/data-grid/data-grid.json
index 6fd1b72c7863f..46f49557431fd 100644
--- a/docs/pages/x/api/data-grid/data-grid.json
+++ b/docs/pages/x/api/data-grid/data-grid.json
@@ -259,6 +259,7 @@
       "columnHeaderDropZone",
       "columnHeaderTitle",
       "columnHeaderTitleContainer",
+      "columnHeaderTitleContainerContent",
       "columnHeaders",
       "columnHeadersInner",
       "columnHeadersInner--scrollable",
diff --git a/docs/translations/api-docs/data-grid/data-grid-pro-pt.json b/docs/translations/api-docs/data-grid/data-grid-pro-pt.json
index 2093ad9cb269b..3922fb93572c7 100644
--- a/docs/translations/api-docs/data-grid/data-grid-pro-pt.json
+++ b/docs/translations/api-docs/data-grid/data-grid-pro-pt.json
@@ -240,6 +240,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/docs/translations/api-docs/data-grid/data-grid-pro-zh.json b/docs/translations/api-docs/data-grid/data-grid-pro-zh.json
index 2093ad9cb269b..3922fb93572c7 100644
--- a/docs/translations/api-docs/data-grid/data-grid-pro-zh.json
+++ b/docs/translations/api-docs/data-grid/data-grid-pro-zh.json
@@ -240,6 +240,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/docs/translations/api-docs/data-grid/data-grid-pro.json b/docs/translations/api-docs/data-grid/data-grid-pro.json
index 2093ad9cb269b..3922fb93572c7 100644
--- a/docs/translations/api-docs/data-grid/data-grid-pro.json
+++ b/docs/translations/api-docs/data-grid/data-grid-pro.json
@@ -240,6 +240,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/docs/translations/api-docs/data-grid/data-grid-pt.json b/docs/translations/api-docs/data-grid/data-grid-pt.json
index 845ea76bf8dc2..98edaa2f1c678 100644
--- a/docs/translations/api-docs/data-grid/data-grid-pt.json
+++ b/docs/translations/api-docs/data-grid/data-grid-pt.json
@@ -209,6 +209,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/docs/translations/api-docs/data-grid/data-grid-zh.json b/docs/translations/api-docs/data-grid/data-grid-zh.json
index 845ea76bf8dc2..98edaa2f1c678 100644
--- a/docs/translations/api-docs/data-grid/data-grid-zh.json
+++ b/docs/translations/api-docs/data-grid/data-grid-zh.json
@@ -209,6 +209,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/docs/translations/api-docs/data-grid/data-grid.json b/docs/translations/api-docs/data-grid/data-grid.json
index 845ea76bf8dc2..98edaa2f1c678 100644
--- a/docs/translations/api-docs/data-grid/data-grid.json
+++ b/docs/translations/api-docs/data-grid/data-grid.json
@@ -209,6 +209,10 @@
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column header's title container element"
     },
+    "columnHeaderTitleContainerContent": {
+      "description": "Styles applied to {{nodeName}}.",
+      "nodeName": "the column header's title excepted buttons"
+    },
     "columnHeaders": {
       "description": "Styles applied to {{nodeName}}.",
       "nodeName": "the column headers"
diff --git a/packages/grid/x-data-grid/src/components/columnHeaders/GridColumnHeaderItem.tsx b/packages/grid/x-data-grid/src/components/columnHeaders/GridColumnHeaderItem.tsx
index 40378758b9cb4..12dfee4184fec 100644
--- a/packages/grid/x-data-grid/src/components/columnHeaders/GridColumnHeaderItem.tsx
+++ b/packages/grid/x-data-grid/src/components/columnHeaders/GridColumnHeaderItem.tsx
@@ -64,6 +64,7 @@ const useUtilityClasses = (ownerState: OwnerState) => {
     ],
     draggableContainer: ['columnHeaderDraggableContainer'],
     titleContainer: ['columnHeaderTitleContainer'],
+    titleContainerContent: ['columnHeaderTitleContainerContent'],
   };
 
   return composeClasses(slots, getDataGridUtilityClass, classes);
@@ -232,13 +233,15 @@ function GridColumnHeaderItem(props: GridColumnHeaderItemProps) {
         {...draggableEventHandlers}
       >
         <div className={classes.titleContainer}>
-          {headerComponent || (
-            <GridColumnHeaderTitle
-              label={column.headerName ?? column.field}
-              description={column.description}
-              columnWidth={width}
-            />
-          )}
+          <div className={classes.titleContainerContent}>
+            {headerComponent || (
+              <GridColumnHeaderTitle
+                label={column.headerName ?? column.field}
+                description={column.description}
+                columnWidth={width}
+              />
+            )}
+          </div>
 
           {columnTitleIconButtons}
         </div>
diff --git a/packages/grid/x-data-grid/src/components/containers/GridRootStyles.ts b/packages/grid/x-data-grid/src/components/containers/GridRootStyles.ts
index 0f4e196f09c4f..a1f15db348342 100644
--- a/packages/grid/x-data-grid/src/components/containers/GridRootStyles.ts
+++ b/packages/grid/x-data-grid/src/components/containers/GridRootStyles.ts
@@ -121,6 +121,11 @@ export const GridRootStyles = styled('div', {
       whiteSpace: 'nowrap',
       overflow: 'hidden',
     },
+    [`& .${gridClasses.columnHeaderTitleContainerContent}`]: {
+      overflow: 'hidden',
+      display: 'flex',
+      alignItems: 'center',
+    },
     [`& .${gridClasses.sortIcon}, & .${gridClasses.filterIcon}`]: {
       fontSize: 'inherit',
     },
diff --git a/packages/grid/x-data-grid/src/constants/gridClasses.ts b/packages/grid/x-data-grid/src/constants/gridClasses.ts
index 659dcafc5b4a4..a1f370d9cf985 100644
--- a/packages/grid/x-data-grid/src/constants/gridClasses.ts
+++ b/packages/grid/x-data-grid/src/constants/gridClasses.ts
@@ -105,6 +105,10 @@ export interface GridClasses {
    * Styles applied to the column header's title container element.
    */
   columnHeaderTitleContainer: string;
+  /**
+   * Styles applied to the column header's title excepted buttons.
+   */
+  columnHeaderTitleContainerContent: string;
   /**
    * Styles applied to the column headers.
    */
@@ -394,6 +398,7 @@ export const gridClasses = generateUtilityClasses('MuiDataGrid', [
   'columnHeaderDropZone',
   'columnHeaderTitle',
   'columnHeaderTitleContainer',
+  'columnHeaderTitleContainerContent',
   'columnHeaders',
   'columnHeadersInner',
   'columnHeadersInner--scrollable',
diff --git a/packages/grid/x-data-grid/src/hooks/features/keyboard/useGridKeyboardNavigation.ts b/packages/grid/x-data-grid/src/hooks/features/keyboard/useGridKeyboardNavigation.ts
index b35b342d62d89..f619849ebaf8c 100644
--- a/packages/grid/x-data-grid/src/hooks/features/keyboard/useGridKeyboardNavigation.ts
+++ b/packages/grid/x-data-grid/src/hooks/features/keyboard/useGridKeyboardNavigation.ts
@@ -8,6 +8,8 @@ import { useGridApiEventHandler } from '../../utils/useGridApiEventHandler';
 import { DataGridProcessedProps } from '../../../models/props/DataGridProps';
 import { gridVisibleSortedRowEntriesSelector } from '../filter/gridFilterSelector';
 import { useCurrentPageRows } from '../../utils/useCurrentPageRows';
+import { GRID_CHECKBOX_SELECTION_COL_DEF } from '../../../colDef/gridCheckboxSelectionColDef';
+import { gridClasses } from '../../../constants/gridClasses';
 
 /**
  * @requires useGridPage (state)
@@ -166,12 +168,21 @@ export const useGridKeyboardNavigation = (
   );
 
   const handleColumnHeaderKeyDown = React.useCallback<
-    GridEventListener<GridEvents.columnHeaderNavigationKeyDown>
+    GridEventListener<GridEvents.columnHeaderKeyDown>
   >(
     (params, event) => {
-      if (!params.field) {
+      const headerTitleNode = event.currentTarget.querySelector(
+        `.${gridClasses.columnHeaderTitleContainerContent}`,
+      );
+      const isFromInsideContent =
+        !!headerTitleNode && headerTitleNode.contains(event.target as Node | null);
+
+      if (isFromInsideContent && params.field !== GRID_CHECKBOX_SELECTION_COL_DEF.field) {
+        // When focus is on a nested input, keyboard events have no effect to avoid conflicts with native events.
+        // There is one exception for the checkBoxHeader
         return;
       }
+
       const dimensions = apiRef.current.getRootDimensions();
       if (!dimensions) {
         return;
diff --git a/packages/grid/x-data-grid/src/tests/keyboard.DataGrid.test.tsx b/packages/grid/x-data-grid/src/tests/keyboard.DataGrid.test.tsx
index 9e723697b7f74..844bb87d079b4 100644
--- a/packages/grid/x-data-grid/src/tests/keyboard.DataGrid.test.tsx
+++ b/packages/grid/x-data-grid/src/tests/keyboard.DataGrid.test.tsx
@@ -1,5 +1,5 @@
 import * as React from 'react';
-import { createRenderer, fireEvent, screen, createEvent } from '@mui/monorepo/test/utils';
+import { createRenderer, fireEvent, screen } from '@mui/monorepo/test/utils';
 import Portal from '@mui/material/Portal';
 import { spy } from 'sinon';
 import { expect } from 'chai';
@@ -365,42 +365,97 @@ describe('<DataGrid /> - Keyboard', () => {
       fireEvent.keyDown(document.activeElement!, { key: 'PageDown' });
       expect(getActiveCell()).to.equal(`5-1`);
     });
-  });
-  /* eslint-enable material-ui/disallow-active-element-as-key-event-target */
 
-  it('should be able to type in an child input', () => {
-    const handleInputKeyDown = spy((event) => event.defaultPrevented);
+    it('should move focus when the focus is on a column header button', function test() {
+      if (isJSDOM) {
+        // This test is not relevant if we can't choose the actual height
+        this.skip();
+      }
 
-    const columns = [
-      {
-        field: 'name',
-        headerName: 'Name',
-        width: 200,
-        renderCell: () => (
-          <input type="text" data-testid="custom-input" onKeyDown={handleInputKeyDown} />
-        ),
-      },
-    ];
+      render(<NavigationTestCaseNoScrollX />);
 
-    const rows = [
-      {
-        id: 1,
-        name: 'John',
-      },
-    ];
+      // get the sort button in column header 1
+      const columnMenuButton = getColumnHeaderCell(1).querySelector(
+        `button[title="Sort"]`,
+      ) as HTMLElement;
 
-    render(
-      <div style={{ width: 300, height: 300 }}>
-        <DataGrid rows={rows} columns={columns} />
-      </div>,
-    );
-    const input = screen.getByTestId('custom-input');
-    fireClickEvent(input);
-    const keydownEvent = createEvent.keyDown(input, {
-      key: 'a',
+      // Simulate click on this button
+      fireEvent.mouseUp(columnMenuButton);
+      fireEvent.click(columnMenuButton);
+      columnMenuButton.focus();
+
+      fireEvent.keyDown(document.activeElement!, { key: 'ArrowDown' });
+      expect(getActiveCell()).to.equal(`0-1`);
+    });
+
+    /* eslint-enable material-ui/disallow-active-element-as-key-event-target */
+    it('should be able to type in an child input', () => {
+      const columns = [
+        {
+          field: 'name',
+          headerName: 'Name',
+          width: 200,
+          renderCell: () => <input type="text" data-testid="custom-input" />,
+        },
+      ];
+
+      const rows = [
+        {
+          id: 1,
+          name: 'John',
+        },
+      ];
+
+      render(
+        <div style={{ width: 300, height: 300 }}>
+          <DataGrid rows={rows} columns={columns} />
+        </div>,
+      );
+      const input = screen.getByTestId('custom-input');
+      fireEvent.mouseUp(input);
+      fireEvent.click(input);
+      input.focus();
+
+      // This does not work with navigation keys.
+      // For now, the workaround for developers is to stop the propagation
+      // But adding input is discouraged, action column or edit mode are better options
+      expect(fireEvent.keyDown(input, { key: 'a' })).to.equal(true);
+    });
+
+    it('should be able to use keyboard in a columnHeader child input', () => {
+      const columns = [
+        {
+          field: 'name',
+          headerName: 'Name',
+          width: 200,
+          renderHeader: () => <input type="text" data-testid="custom-input" />,
+        },
+      ];
+
+      const rows = [
+        {
+          id: 1,
+          name: 'John',
+        },
+      ];
+
+      render(
+        <div style={{ width: 300, height: 300 }}>
+          <DataGrid rows={rows} columns={columns} />
+        </div>,
+      );
+      const input = screen.getByTestId('custom-input');
+      fireEvent.mouseUp(input);
+      fireEvent.click(input);
+      input.focus();
+
+      // Verify that the event is not prevented during the bubbling.
+      // fireEvent.keyDown return false if it is the case
+      // For more info, see the related discussion: https://github.com/mui/mui-x/pull/3624#discussion_r787767632
+      expect(fireEvent.keyDown(input, { key: 'a' })).to.equal(true);
+      expect(fireEvent.keyDown(input, { key: ' ' })).to.equal(true);
+      expect(fireEvent.keyDown(input, { key: 'ArrowLeft' })).to.equal(true);
     });
-    fireEvent(input, keydownEvent);
-    expect(handleInputKeyDown.returnValues).to.deep.equal([false]);
   });
 
   it('should ignore events coming from a portal inside the cell', () => {