diff --git a/packages/block-editor/src/components/block-mover/index.js b/packages/block-editor/src/components/block-mover/index.js
index 0c6417a9c02c52..0055a7d47230b6 100644
--- a/packages/block-editor/src/components/block-mover/index.js
+++ b/packages/block-editor/src/components/block-mover/index.js
@@ -13,6 +13,7 @@ import { ToolbarGroup, ToolbarItem, Button } from '@wordpress/components';
 import { getBlockType } from '@wordpress/blocks';
 import { useState } from '@wordpress/element';
 import { withSelect } from '@wordpress/data';
+import { __ } from '@wordpress/i18n';
 
 /**
  * Internal dependencies
@@ -39,6 +40,9 @@ function BlockMover( {
 		return null;
 	}
 
+	const label =
+		clientIds.length === 1 ? __( 'Drag Block' ) : __( 'Drag Blocks' );
+
 	// We emulate a disabled state because forcefully applying the `disabled`
 	// attribute on the buttons while it has focus causes the screen to change
 	// to an unfocused state (body as active element) without firing blur on,
@@ -60,6 +64,7 @@ function BlockMover( {
 							icon={ dragHandle }
 							className="block-editor-block-mover__drag-handle"
 							aria-hidden="true"
+							label={ label }
 							// Should not be able to tab to drag handle as this
 							// button can only be used with a pointer device.
 							tabIndex="-1"