diff --git a/packages/block-library/src/quote/index.js b/packages/block-library/src/quote/index.js
index 78e53875b771db..d3f020a220c3db 100644
--- a/packages/block-library/src/quote/index.js
+++ b/packages/block-library/src/quote/index.js
@@ -100,7 +100,12 @@ export const settings = {
 			},
 			{
 				type: 'raw',
-				selector: 'blockquote',
+				isMatch: ( node ) => (
+					node.nodeName === 'BLOCKQUOTE' &&
+					// The quote block can only handle multiline paragraph
+					// content.
+					Array.from( node.childNodes ).every( ( child ) => child.nodeName === 'P' )
+				),
 				schema: {
 					blockquote: {
 						children: {
diff --git a/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap b/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap
index 1fbb36f44d9abe..320b201a836e3c 100644
--- a/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap
+++ b/test/integration/__snapshots__/blocks-raw-handling.spec.js.snap
@@ -44,5 +44,13 @@ exports[`Blocks raw handling rawHandler should convert HTML post to blocks with
 
 <!-- wp:list {\\"ordered\\":true} -->
 <ol><li>Item</li></ol>
-<!-- /wp:list -->"
+<!-- /wp:list -->
+
+<!-- wp:quote -->
+<blockquote class=\\"wp-block-quote\\"><p>Text.</p></blockquote>
+<!-- /wp:quote -->
+
+<!-- wp:html -->
+<blockquote><h1>Heading</h1><p>Text.</p></blockquote>
+<!-- /wp:html -->"
 `;
diff --git a/test/integration/fixtures/wordpress-convert.html b/test/integration/fixtures/wordpress-convert.html
index 0a8a20c6e19b12..0fe1de21dc6621 100644
--- a/test/integration/fixtures/wordpress-convert.html
+++ b/test/integration/fixtures/wordpress-convert.html
@@ -23,3 +23,16 @@ <h3>Shortcode</h3>
 	  <li>Item</li>
 	</ol>
 </ol>
+
+<!-- Quote with paragraphs -->
+
+<blockquote>
+	<p>Text.</p>
+</blockquote>
+
+<!-- Quote with more than paragraphs -->
+
+<blockquote>
+	<h1>Heading</h1>
+	<p>Text.</p>
+</blockquote>