diff --git a/packages/block-library/src/embed/editor.scss b/packages/block-library/src/embed/editor.scss
index 29cbd9fb932cff..af0b050764ce77 100644
--- a/packages/block-library/src/embed/editor.scss
+++ b/packages/block-library/src/embed/editor.scss
@@ -31,3 +31,12 @@
 		word-break: break-word;
 	}
 }
+
+.block-library-embed__interactive-overlay {
+	position: absolute;
+	top: 0;
+	left: 0;
+	right: 0;
+	bottom: 0;
+	opacity: 0;
+}
diff --git a/packages/block-library/src/embed/embed-preview.js b/packages/block-library/src/embed/embed-preview.js
index efc11b7a5809ba..cf8d35460ae3df 100644
--- a/packages/block-library/src/embed/embed-preview.js
+++ b/packages/block-library/src/embed/embed-preview.js
@@ -17,58 +17,101 @@ import classnames from 'classnames/dedupe';
 import { __, sprintf } from '@wordpress/i18n';
 import { Placeholder, SandBox } from '@wordpress/components';
 import { RichText, BlockIcon } from '@wordpress/editor';
+import { Component } from '@wordpress/element';
 
 /**
  * Internal dependencies
  */
 import WpEmbedPreview from './wp-embed-preview';
 
-const EmbedPreview = ( props ) => {
-	const { preview, url, type, caption, onCaptionChange, isSelected, className, icon, label } = props;
-	const { scripts } = preview;
+class EmbedPreview extends Component {
+	constructor() {
+		super( ...arguments );
+		this.hideOverlay = this.hideOverlay.bind( this );
+		this.state = {
+			interactive: false,
+		};
+	}
 
-	const html = 'photo' === type ? getPhotoHtml( preview ) : preview.html;
-	const parsedHost = parse( url ).host.split( '.' );
-	const parsedHostBaseUrl = parsedHost.splice( parsedHost.length - 2, parsedHost.length - 1 ).join( '.' );
-	const cannotPreview = includes( HOSTS_NO_PREVIEWS, parsedHostBaseUrl );
-	// translators: %s: host providing embed content e.g: www.youtube.com
-	const iframeTitle = sprintf( __( 'Embedded content from %s' ), parsedHostBaseUrl );
-	const sandboxClassnames = classnames( type, className, 'wp-block-embed__wrapper' );
+	static getDerivedStateFromProps( nextProps, state ) {
+		if ( ! nextProps.isSelected && state.interactive ) {
+			// We only want to change this when the block is not selected, because changing it when
+			// the block becomes selected makes the overlap disappear too early. Hiding the overlay
+			// happens on mouseup when the overlay is clicked.
+			return { interactive: false };
+		}
 
-	const embedWrapper = 'wp-embed' === type ? (
-		<WpEmbedPreview
-			html={ html }
-		/>
-	) : (
-		<div className="wp-block-embed__wrapper">
-			<SandBox
+		return null;
+	}
+
+	hideOverlay() {
+		// This is called onMouseUp on the overlay. We can't respond to the `isSelected` prop
+		// changing, because that happens on mouse down, and the overlay immediately disappears,
+		// and the mouse event can end up in the preview content. We can't use onClick on
+		// the overlay to hide it either, because then the editor misses the mouseup event, and
+		// thinks we're multi-selecting blocks.
+		this.setState( { interactive: true } );
+	}
+
+	render() {
+		const { preview, url, type, caption, onCaptionChange, isSelected, className, icon, label } = this.props;
+		const { scripts } = preview;
+		const { interactive } = this.state;
+
+		const html = 'photo' === type ? getPhotoHtml( preview ) : preview.html;
+		const parsedHost = parse( url ).host.split( '.' );
+		const parsedHostBaseUrl = parsedHost.splice( parsedHost.length - 2, parsedHost.length - 1 ).join( '.' );
+		const cannotPreview = includes( HOSTS_NO_PREVIEWS, parsedHostBaseUrl );
+		// translators: %s: host providing embed content e.g: www.youtube.com
+		const iframeTitle = sprintf( __( 'Embedded content from %s' ), parsedHostBaseUrl );
+		const sandboxClassnames = classnames( type, className, 'wp-block-embed__wrapper' );
+
+		// Disabled because the overlay div doesn't actually have a role or functionality
+		// as far as the user is concerned. We're just catching the first click so that
+		// the block can be selected without interacting with the embed preview that the overlay covers.
+		/* eslint-disable jsx-a11y/no-noninteractive-element-interactions */
+		/* eslint-disable jsx-a11y/no-static-element-interactions */
+		const embedWrapper = 'wp-embed' === type ? (
+			<WpEmbedPreview
 				html={ html }
-				scripts={ scripts }
-				title={ iframeTitle }
-				type={ sandboxClassnames }
 			/>
-		</div>
-	);
-
-	return (
-		<figure className={ classnames( className, 'wp-block-embed', { 'is-type-video': 'video' === type } ) }>
-			{ ( cannotPreview ) ? (
-				<Placeholder icon={ <BlockIcon icon={ icon } showColors /> } label={ label }>
-					<p className="components-placeholder__error"><a href={ url }>{ url }</a></p>
-					<p className="components-placeholder__error">{ __( 'Sorry, this embedded content cannot be previewed in the editor.' ) }</p>
-				</Placeholder>
-			) : embedWrapper }
-			{ ( ! RichText.isEmpty( caption ) || isSelected ) && (
-				<RichText
-					tagName="figcaption"
-					placeholder={ __( 'Write caption…' ) }
-					value={ caption }
-					onChange={ onCaptionChange }
-					inlineToolbar
+		) : (
+			<div className="wp-block-embed__wrapper">
+				<SandBox
+					html={ html }
+					scripts={ scripts }
+					title={ iframeTitle }
+					type={ sandboxClassnames }
+					onFocus={ this.hideOverlay }
 				/>
-			) }
-		</figure>
-	);
-};
+				{ ! interactive && <div
+					className="block-library-embed__interactive-overlay"
+					onMouseUp={ this.hideOverlay } /> }
+			</div>
+		);
+		/* eslint-enable jsx-a11y/no-static-element-interactions */
+		/* eslint-enable jsx-a11y/no-noninteractive-element-interactions */
+
+		return (
+			<figure className={ classnames( className, 'wp-block-embed', { 'is-type-video': 'video' === type } ) }>
+				{ ( cannotPreview ) ? (
+					<Placeholder icon={ <BlockIcon icon={ icon } showColors /> } label={ label }>
+						<p className="components-placeholder__error"><a href={ url }>{ url }</a></p>
+						<p className="components-placeholder__error">{ __( 'Sorry, this embedded content cannot be previewed in the editor.' ) }</p>
+					</Placeholder>
+				) : embedWrapper }
+				{ ( ! RichText.isEmpty( caption ) || isSelected ) && (
+					<RichText
+						tagName="figcaption"
+						placeholder={ __( 'Write caption…' ) }
+						value={ caption }
+						onChange={ onCaptionChange }
+						inlineToolbar
+					/>
+				) }
+			</figure>
+		);
+	}
+}
 
 export default EmbedPreview;
diff --git a/packages/components/src/sandbox/index.js b/packages/components/src/sandbox/index.js
index 1862c00db97540..01f2e8f8e3b7fd 100644
--- a/packages/components/src/sandbox/index.js
+++ b/packages/components/src/sandbox/index.js
@@ -198,7 +198,7 @@ class Sandbox extends Component {
 	}
 
 	render() {
-		const { title } = this.props;
+		const { title, onFocus } = this.props;
 
 		return (
 			<FocusableIframe
@@ -207,6 +207,7 @@ class Sandbox extends Component {
 				className="components-sandbox"
 				sandbox="allow-scripts allow-same-origin allow-presentation"
 				onLoad={ this.trySandbox }
+				onFocus={ onFocus }
 				width={ Math.ceil( this.state.width ) }
 				height={ Math.ceil( this.state.height ) } />
 		);