diff --git a/src/wp-includes/block-editor.php b/src/wp-includes/block-editor.php
index e8900d1ccdc1a..71d95aff5ca8a 100644
--- a/src/wp-includes/block-editor.php
+++ b/src/wp-includes/block-editor.php
@@ -665,6 +665,8 @@ function get_block_editor_settings( array $custom_settings, $block_editor_contex
 		}
 	}
 
+	$editor_settings['canUpdateBlockBindings'] = current_user_can( 'edit_block_binding', $block_editor_context );
+
 	/**
 	 * Filters the settings to pass to the block editor for all editor type.
 	 *
diff --git a/src/wp-includes/capabilities.php b/src/wp-includes/capabilities.php
index d420717bc759b..dab0067f63858 100644
--- a/src/wp-includes/capabilities.php
+++ b/src/wp-includes/capabilities.php
@@ -801,6 +801,32 @@ function map_meta_cap( $cap, $user_id, ...$args ) {
 		case 'delete_app_password':
 			$caps = map_meta_cap( 'edit_user', $user_id, $args[0] );
 			break;
+		case 'edit_block_binding':
+			$block_editor_context = $args[0];
+			if ( isset( $block_editor_context->post ) ) {
+				$object_id = $block_editor_context->post->ID;
+			}
+			/*
+			 * If the post ID is null, check if the context is the site editor.
+			 * Fall back to the edit_theme_options in that case.
+			 */
+			if ( ! isset( $object_id ) ) {
+				if ( ! isset( $block_editor_context->name ) || 'core/edit-site' !== $block_editor_context->name ) {
+					$caps[] = 'do_not_allow';
+					break;
+				}
+				$caps = map_meta_cap( 'edit_theme_options', $user_id );
+				break;
+			}
+
+			$object_subtype = get_object_subtype( 'post', (int) $object_id );
+			if ( empty( $object_subtype ) ) {
+				$caps[] = 'do_not_allow';
+				break;
+			}
+
+			$caps = map_meta_cap( "edit_{$object_subtype}", $user_id, $object_id );
+			break;
 		default:
 			// Handle meta capabilities for custom post types.
 			global $post_type_meta_caps;
diff --git a/tests/phpunit/tests/user/capabilities.php b/tests/phpunit/tests/user/capabilities.php
index 473b0417ba198..afaf3d54f7e03 100644
--- a/tests/phpunit/tests/user/capabilities.php
+++ b/tests/phpunit/tests/user/capabilities.php
@@ -570,7 +570,8 @@ public function testMetaCapsTestsAreCorrect() {
 			$expected['read_app_password'],
 			$expected['edit_app_password'],
 			$expected['delete_app_passwords'],
-			$expected['delete_app_password']
+			$expected['delete_app_password'],
+			$expected['edit_block_binding']
 		);
 
 		$expected = array_keys( $expected );
@@ -2376,4 +2377,52 @@ public function data_block_caps() {
 
 		return $data;
 	}
+
+	/**
+	 * Test `edit_block_binding` meta capability is properly mapped.
+	 *
+	 * @ticket 61945
+	 */
+	public function test_edit_block_binding_caps_are_mapped_correctly() {
+		$author = self::$users['administrator'];
+		$post   = self::factory()->post->create_and_get(
+			array(
+				'post_author' => $author->ID,
+				'post_type'   => 'post',
+			)
+		);
+
+		foreach ( self::$users as $role => $user ) {
+			// It should map to `edit_{post_type}` if editing a post.
+			$this->assertSame(
+				user_can( $user->ID, 'edit_post', $post->ID ),
+				user_can(
+					$user->ID,
+					'edit_block_binding',
+					new WP_Block_Editor_Context(
+						array(
+							'post' => $post,
+							'name' => 'core/edit-post',
+						)
+					)
+				),
+				"Role: {$role} in post editing"
+			);
+			// It should map to `edit_theme_options` if editing a template.
+			$this->assertSame(
+				user_can( $user->ID, 'edit_theme_options' ),
+				user_can(
+					$user->ID,
+					'edit_block_binding',
+					new WP_Block_Editor_Context(
+						array(
+							'post' => null,
+							'name' => 'core/edit-site',
+						)
+					)
+				),
+				"Role: {$role} in template editing"
+			);
+		}
+	}
 }