diff --git a/test/e2e/specs/block-mover.test.js b/test/e2e/specs/block-mover.test.js
new file mode 100644
index 0000000000000..5d1b77707c244
--- /dev/null
+++ b/test/e2e/specs/block-mover.test.js
@@ -0,0 +1,40 @@
+/**
+ * Internal dependencies
+ */
+import '../support/bootstrap';
+import { newPost, newDesktopBrowserPage } from '../support/utils';
+
+describe( 'block mover', () => {
+	beforeEach( async () => {
+		await newDesktopBrowserPage();
+		await newPost();
+	} );
+
+	it( 'should show block mover when more than one block exists', async () => {
+		// Create a two blocks on the page.
+		await page.click( '.editor-default-block-appender' );
+		await page.keyboard.type( 'First Paragraph' );
+		await page.keyboard.press( 'Enter' );
+		await page.keyboard.type( 'Second Paragraph' );
+
+		// Select a block so the block mover is rendered.
+		await page.focus( '.editor-block-list__block' );
+
+		const blockMover = await page.$$( '.editor-block-mover' );
+		// There should be a block mover.
+		expect( blockMover ).toHaveLength( 1 );
+	} );
+
+	it( 'should hide block mover when only one block exists', async () => {
+		// Create a single block on the page.
+		await page.click( '.editor-default-block-appender' );
+		await page.keyboard.type( 'First Paragraph' );
+
+		// Select a block so the block mover has the possibility of being rendered.
+		await page.focus( '.editor-block-list__block' );
+
+		// Ensure no block mover exists when only one block exists on the page.
+		const blockMover = await page.$$( '.editor-block-mover' );
+		expect( blockMover ).toHaveLength( 0 );
+	} );
+} );