diff --git a/cpp/open3d/geometry/PointCloud.cpp b/cpp/open3d/geometry/PointCloud.cpp
index 3e55bc3acd6..b0b6e0130ae 100644
--- a/cpp/open3d/geometry/PointCloud.cpp
+++ b/cpp/open3d/geometry/PointCloud.cpp
@@ -541,23 +541,25 @@ std::shared_ptr<PointCloud> PointCloud::FarthestPointDownSample(
     return SelectByIndex(selected_indices);
 }
 
-std::shared_ptr<PointCloud> PointCloud::Crop(
-        const AxisAlignedBoundingBox &bbox) const {
+std::shared_ptr<PointCloud> PointCloud::Crop(const AxisAlignedBoundingBox &bbox,
+                                             bool invert) const {
     if (bbox.IsEmpty()) {
         utility::LogError(
                 "AxisAlignedBoundingBox either has zeros size, or has wrong "
                 "bounds.");
     }
-    return SelectByIndex(bbox.GetPointIndicesWithinBoundingBox(points_));
+    return SelectByIndex(bbox.GetPointIndicesWithinBoundingBox(points_),
+                         invert);
 }
-std::shared_ptr<PointCloud> PointCloud::Crop(
-        const OrientedBoundingBox &bbox) const {
+std::shared_ptr<PointCloud> PointCloud::Crop(const OrientedBoundingBox &bbox,
+                                             bool invert) const {
     if (bbox.IsEmpty()) {
         utility::LogError(
                 "AxisAlignedBoundingBox either has zeros size, or has wrong "
                 "bounds.");
     }
-    return SelectByIndex(bbox.GetPointIndicesWithinBoundingBox(points_));
+    return SelectByIndex(bbox.GetPointIndicesWithinBoundingBox(points_),
+                         invert);
 }
 
 std::tuple<std::shared_ptr<PointCloud>, std::vector<size_t>>
diff --git a/cpp/open3d/geometry/PointCloud.h b/cpp/open3d/geometry/PointCloud.h
index b55840106b6..334bdc9f0f5 100644
--- a/cpp/open3d/geometry/PointCloud.h
+++ b/cpp/open3d/geometry/PointCloud.h
@@ -185,7 +185,9 @@ class PointCloud : public Geometry3D {
     /// clipped.
     ///
     /// \param bbox AxisAlignedBoundingBox to crop points.
-    std::shared_ptr<PointCloud> Crop(const AxisAlignedBoundingBox &bbox) const;
+    /// \param invert Optional boolean to invert cropping.
+    std::shared_ptr<PointCloud> Crop(const AxisAlignedBoundingBox &bbox,
+                                     bool invert = false) const;
 
     /// \brief Function to crop pointcloud into output pointcloud
     ///
@@ -193,7 +195,9 @@ class PointCloud : public Geometry3D {
     /// clipped.
     ///
     /// \param bbox OrientedBoundingBox to crop points.
-    std::shared_ptr<PointCloud> Crop(const OrientedBoundingBox &bbox) const;
+    /// \param invert Optional boolean to invert cropping.
+    std::shared_ptr<PointCloud> Crop(const OrientedBoundingBox &bbox,
+                                     bool invert = false) const;
 
     /// \brief Function to remove points that have less than \p nb_points in a
     /// sphere of a given radius.
diff --git a/cpp/pybind/geometry/pointcloud.cpp b/cpp/pybind/geometry/pointcloud.cpp
index d9e2ce935c6..835ec3123b1 100644
--- a/cpp/pybind/geometry/pointcloud.cpp
+++ b/cpp/pybind/geometry/pointcloud.cpp
@@ -86,16 +86,16 @@ void pybind_pointcloud(py::module &m) {
                  "num_samples"_a)
             .def("crop",
                  (std::shared_ptr<PointCloud>(PointCloud::*)(
-                         const AxisAlignedBoundingBox &) const) &
+                         const AxisAlignedBoundingBox &, bool) const) &
                          PointCloud::Crop,
                  "Function to crop input pointcloud into output pointcloud",
-                 "bounding_box"_a)
+                 "bounding_box"_a, "invert"_a = false)
             .def("crop",
                  (std::shared_ptr<PointCloud>(PointCloud::*)(
-                         const OrientedBoundingBox &) const) &
+                         const OrientedBoundingBox &, bool) const) &
                          PointCloud::Crop,
                  "Function to crop input pointcloud into output pointcloud",
-                 "bounding_box"_a)
+                 "bounding_box"_a, "invert"_a = false)
             .def("remove_non_finite_points", &PointCloud::RemoveNonFinitePoints,
                  "Removes all points from the point cloud that have a nan "
                  "entry, or infinite entries. It also removes the "
@@ -289,7 +289,8 @@ camera. Given depth value d at (u, v) image coordinate, the corresponding 3d poi
               "number of points[0-1]"}});
     docstring::ClassMethodDocInject(
             m, "PointCloud", "crop",
-            {{"bounding_box", "AxisAlignedBoundingBox to crop points"}});
+            {{"bounding_box", "AxisAlignedBoundingBox to crop points"},
+             {"invert", "optional boolean to invert cropping"}});
     docstring::ClassMethodDocInject(
             m, "PointCloud", "remove_non_finite_points",
             {{"remove_nan", "Remove NaN values from the PointCloud"},
diff --git a/cpp/tests/geometry/PointCloud.cpp b/cpp/tests/geometry/PointCloud.cpp
index 379b8ad0941..21bfe5659bf 100644
--- a/cpp/tests/geometry/PointCloud.cpp
+++ b/cpp/tests/geometry/PointCloud.cpp
@@ -982,6 +982,38 @@ TEST(PointCloud, Crop_OrientedBoundingBox) {
                                     }));
 }
 
+TEST(PointCloud, Crop_AxisAlignedBoundingBox_Invert) {
+    geometry::AxisAlignedBoundingBox aabb({0, 0, 0}, {2, 2, 2});
+    geometry::PointCloud pcd({{0, 0, 0},
+                              {2, 2, 2},
+                              {1, 1, 1},
+                              {1, 1, 2},
+                              {3, 1, 1},
+                              {-1, 1, 1}});
+    pcd.normals_ = {{0, 0, 0}, {1, 0, 0}, {2, 0, 0},
+                    {3, 0, 0}, {4, 0, 0}, {5, 0, 0}};
+    pcd.colors_ = {{0.0, 0.0, 0.0}, {0.1, 0.0, 0.0}, {0.2, 0.0, 0.0},
+                   {0.3, 0.0, 0.0}, {0.4, 0.0, 0.0}, {0.5, 0.0, 0.0}};
+    pcd.covariances_ = {
+            0.0 * Eigen::Matrix3d::Identity(),
+            1.0 * Eigen::Matrix3d::Identity(),
+            2.0 * Eigen::Matrix3d::Identity(),
+            3.0 * Eigen::Matrix3d::Identity(),
+            4.0 * Eigen::Matrix3d::Identity(),
+            5.0 * Eigen::Matrix3d::Identity(),
+    };
+    std::shared_ptr<geometry::PointCloud> pc_crop = pcd.Crop(aabb, true);
+    ExpectEQ(pc_crop->points_,
+             std::vector<Eigen::Vector3d>({{3, 1, 1}, {-1, 1, 1}}));
+    ExpectEQ(pc_crop->normals_,
+             std::vector<Eigen::Vector3d>({{4, 0, 0}, {5, 0, 0}}));
+    ExpectEQ(pc_crop->colors_,
+             std::vector<Eigen::Vector3d>({{0.4, 0.0, 0.0}, {0.5, 0.0, 0.0}}));
+    ExpectEQ(pc_crop->covariances_,
+             std::vector<Eigen::Matrix3d>({4.0 * Eigen::Matrix3d::Identity(),
+                                           5.0 * Eigen::Matrix3d::Identity()}));
+}
+
 TEST(PointCloud, EstimateNormals) {
     geometry::PointCloud pcd({
             {0, 0, 0},