diff --git a/packages/editor/src/components/block-mover/drag-handle.js b/packages/editor/src/components/block-mover/drag-handle.js
index 5f7584c29744b..aa7e1efaf33f7 100644
--- a/packages/editor/src/components/block-mover/drag-handle.js
+++ b/packages/editor/src/components/block-mover/drag-handle.js
@@ -8,7 +8,7 @@ import classnames from 'classnames';
  */
 import { IconButton, Draggable } from '@wordpress/components';
 
-export const IconDragHandle = ( { isVisible, className, icon, label, onFocus, onBlur, onDragStart, onDragEnd, blockElementId, order, rootClientId, clientId, layout } ) => {
+export const IconDragHandle = ( { isVisible, className, icon, onFocus, onBlur, onDragStart, onDragEnd, blockElementId, order, rootClientId, clientId, layout } ) => {
 	if ( ! isVisible ) {
 		return null;
 	}
@@ -33,7 +33,10 @@ export const IconDragHandle = ( { isVisible, className, icon, label, onFocus, on
 					<IconButton
 						className={ dragHandleClassNames }
 						icon={ icon }
-						label={ label }
+						aria-hidden="true"
+						focusable="false"
+						aria-label=""
+						tabIndex="-1"
 						onFocus={ onFocus }
 						onBlur={ onBlur }
 						onDragStart={ onDraggableStart }
diff --git a/packages/editor/src/components/block-mover/style.scss b/packages/editor/src/components/block-mover/style.scss
index 9d569b8a6a310..ad75de84aedfa 100644
--- a/packages/editor/src/components/block-mover/style.scss
+++ b/packages/editor/src/components/block-mover/style.scss
@@ -93,6 +93,17 @@
 .editor-block-mover__control-drag-handle {
 	cursor: move; // Fallback for IE/Edge < 14
 	cursor: grab;
+
+	&:not(:disabled):not([aria-disabled="true"]):not(.is-default):hover,
+	&:not(:disabled):not([aria-disabled="true"]):not(.is-default):active,
+	&:not(:disabled):not([aria-disabled="true"]):not(.is-default):focus {
+		box-shadow: none;
+		background: none;
+	}
+
+	&:not(:disabled):not([aria-disabled="true"]):not(.is-default):active {
+		cursor: grabbing;
+	}
 }
 
 .editor-block-mover__description {