diff --git a/packages/block-editor/src/components/block-list/block.js b/packages/block-editor/src/components/block-list/block.js
index a95075c6f9b42..ff5915981acdf 100644
--- a/packages/block-editor/src/components/block-list/block.js
+++ b/packages/block-editor/src/components/block-list/block.js
@@ -161,6 +161,10 @@ function BlockListBlock( {
 		!! wrapperProps[ 'data-align' ] &&
 		! themeSupportsLayout;
 
+	// Support for sticky position in classic themes with alignment wrappers.
+
+	const isSticky = className?.includes( 'is-position-sticky' );
+
 	// For aligned blocks, provide a wrapper element so the block can be
 	// positioned relative to the block column.
 	// This is only kept for classic themes that don't support layout
@@ -172,7 +176,7 @@ function BlockListBlock( {
 	if ( isAligned ) {
 		blockEdit = (
 			<div
-				className="wp-block"
+				className={ classnames( 'wp-block', isSticky && className ) }
 				data-align={ wrapperProps[ 'data-align' ] }
 			>
 				{ blockEdit }
@@ -221,7 +225,7 @@ function BlockListBlock( {
 					isTemporarilyEditingAsBlocks,
 			},
 			dataAlign && themeSupportsLayout && `align${ dataAlign }`,
-			className
+			! ( dataAlign && isSticky ) && className
 		),
 		wrapperProps: restWrapperProps,
 		isAligned,