diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
index 26f462e4f3..f66a3d351b 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
@@ -558,6 +558,11 @@ class WP_REST_Attachments_Controller extends WP_REST_Posts_Controller {
 			'type'     => $type,
 		);
 
+		$size_check = self::check_upload_size( $file_data );
+		if ( is_wp_error( $size_check ) ) {
+			return $size_check;
+		}
+
 		$overrides = array(
 			'test_form' => false,
 		);
@@ -725,6 +730,11 @@ class WP_REST_Attachments_Controller extends WP_REST_Posts_Controller {
 			$overrides['action'] = 'wp_handle_mock_upload';
 		}
 
+		$size_check = self::check_upload_size( $files['file'] );
+		if ( is_wp_error( $size_check ) ) {
+			return $size_check;
+		}
+
 		/** Include admin functions to get access to wp_handle_upload() */
 		require_once ABSPATH . 'wp-admin/includes/admin.php';
 
@@ -762,4 +772,42 @@ class WP_REST_Attachments_Controller extends WP_REST_Posts_Controller {
 		return $media_types;
 	}
 
+	/**
+	 * Determine if uploaded file exceeds space quota on multisite.
+	 *
+	 * Replicates check_upload_size().
+	 *
+	 * @since 4.9.8
+	 *
+	 * @param array $file $_FILES array for a given file.
+	 * @return true|WP_Error True if can upload, error for errors.
+	 */
+	protected function check_upload_size( $file ) {
+		if ( ! is_multisite() ) {
+			return true;
+		}
+
+		if ( get_site_option( 'upload_space_check_disabled' ) ) {
+			return true;
+		}
+
+		$space_left = get_upload_space_available();
+
+		$file_size = filesize( $file['tmp_name'] );
+		if ( $space_left < $file_size ) {
+			/* translators: %s: required disk space in kilobytes */
+			return new WP_Error( 'rest_upload_limited_space', sprintf( __( 'Not enough space to upload. %s KB needed.' ), number_format( ( $file_size - $space_left ) / KB_IN_BYTES ) ), array( 'status' => 400 ) );
+		}
+
+		if ( $file_size > ( KB_IN_BYTES * get_site_option( 'fileupload_maxk', 1500 ) ) ) {
+			/* translators: %s: maximum allowed file size in kilobytes */
+			return new WP_Error( 'rest_upload_file_too_big', sprintf( __( 'This file is too big. Files must be less than %s KB in size.' ), get_site_option( 'fileupload_maxk', 1500 ) ), array( 'status' => 400 ) );
+		}
+
+		if ( upload_is_user_over_quota( false ) ) {
+			return new WP_Error( 'rest_upload_user_quota_exceeded', __( 'You have used your space quota. Please delete files before uploading.' ), array( 'status' => 400 ) );
+		}
+		return true;
+	}
+
 }
diff --git a/tests/phpunit/tests/rest-api/rest-attachments-controller.php b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
index c42e40f194..4fa9b19183 100644
--- a/tests/phpunit/tests/rest-api/rest-attachments-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
@@ -1388,4 +1388,106 @@ class WP_Test_REST_Attachments_Controller extends WP_Test_REST_Post_Type_Control
 
 	}
 
+	/**
+	 * @ticket 43751
+	 * @group multisite
+	 * @group ms-required
+	 */
+	public function test_create_item_with_file_exceeds_multisite_max_filesize() {
+		wp_set_current_user( self::$author_id );
+		update_site_option( 'fileupload_maxk', 1 );
+		update_site_option( 'upload_space_check_disabled', false );
+
+		$request = new WP_REST_Request( 'POST', '/wp/v2/media' );
+		$request->set_file_params(
+			array(
+				'file' => array(
+					'error'    => '0',
+					'file'     => file_get_contents( $this->test_file ),
+					'name'     => 'canola.jpg',
+					'size'     => filesize( $this->test_file ),
+					'tmp_name' => $this->test_file,
+				),
+			)
+		);
+		$request->set_param( 'title', 'My title is very cool' );
+		$request->set_param( 'caption', 'This is a better caption.' );
+		$request->set_header( 'Content-MD5', md5_file( $this->test_file ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$this->assertErrorResponse( 'rest_upload_file_too_big', $response, 400 );
+	}
+
+	/**
+	 * @ticket 43751
+	 * @group multisite
+	 * @group ms-required
+	 */
+	public function test_create_item_with_data_exceeds_multisite_max_filesize() {
+		wp_set_current_user( self::$author_id );
+		update_site_option( 'fileupload_maxk', 1 );
+		update_site_option( 'upload_space_check_disabled', false );
+
+		$request = new WP_REST_Request( 'POST', '/wp/v2/media' );
+		$request->set_header( 'Content-Type', 'image/jpeg' );
+		$request->set_header( 'Content-Disposition', 'attachment; filename=canola.jpg' );
+		$request->set_body( file_get_contents( $this->test_file ) );
+		$request->set_param( 'title', 'My title is very cool' );
+		$request->set_param( 'caption', 'This is a better caption.' );
+
+		$response = rest_get_server()->dispatch( $request );
+		$this->assertErrorResponse( 'rest_upload_file_too_big', $response, 400 );
+	}
+
+	/**
+	 * @ticket 43751
+	 * @group multisite
+	 * @group ms-required
+	 */
+	public function test_create_item_with_file_exceeds_multisite_site_upload_space() {
+		wp_set_current_user( self::$author_id );
+		add_filter( 'get_space_allowed', '__return_zero' );
+		update_site_option( 'upload_space_check_disabled', false );
+
+		$request = new WP_REST_Request( 'POST', '/wp/v2/media' );
+		$request->set_file_params(
+			array(
+				'file' => array(
+					'error'    => '0',
+					'file'     => file_get_contents( $this->test_file ),
+					'name'     => 'canola.jpg',
+					'size'     => filesize( $this->test_file ),
+					'tmp_name' => $this->test_file,
+				),
+			)
+		);
+		$request->set_param( 'title', 'My title is very cool' );
+		$request->set_param( 'caption', 'This is a better caption.' );
+		$request->set_header( 'Content-MD5', md5_file( $this->test_file ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$this->assertErrorResponse( 'rest_upload_limited_space', $response, 400 );
+	}
+
+	/**
+	 * @ticket 43751
+	 * @group multisite
+	 * @group ms-required
+	 */
+	public function test_create_item_with_data_exceeds_multisite_site_upload_space() {
+		wp_set_current_user( self::$author_id );
+		add_filter( 'get_space_allowed', '__return_zero' );
+		update_site_option( 'upload_space_check_disabled', false );
+
+		$request = new WP_REST_Request( 'POST', '/wp/v2/media' );
+		$request->set_header( 'Content-Type', 'image/jpeg' );
+		$request->set_header( 'Content-Disposition', 'attachment; filename=canola.jpg' );
+		$request->set_body( file_get_contents( $this->test_file ) );
+		$request->set_param( 'title', 'My title is very cool' );
+		$request->set_param( 'caption', 'This is a better caption.' );
+
+		$response = rest_get_server()->dispatch( $request );
+		$this->assertErrorResponse( 'rest_upload_limited_space', $response, 400 );
+	}
+
 }