Index: src/wp-admin/includes/class-wp-posts-list-table.php
===================================================================
--- src/wp-admin/includes/class-wp-posts-list-table.php	(revision 26901)
+++ src/wp-admin/includes/class-wp-posts-list-table.php	(working copy)
@@ -561,7 +561,16 @@
 				if ( $format = get_post_format( $post->ID ) ) {
 					$label = get_post_format_string( $format );
 
-					echo '<a href="' . esc_url( add_query_arg( array( 'post_format' => $format, 'post_type' => $post->post_type ), 'edit.php' ) ) . '" class="post-state-format post-format-icon post-format-' . $format . '" title="' . $label . '">' . $label . ":</a> ";
+					/**
+					 * Filter whether to display a post format icon for the post.
+					 *
+					 * @since 3.9.0
+					 *
+					 * @param bool $show Whether to display the post format icon. Default true.
+					 */
+					if ( apply_filters( 'post_row_format_enabled', true ) ) {
+						echo '<a href="' . esc_url( add_query_arg( array( 'post_format' => $format, 'post_type' => $post->post_type ), 'edit.php' ) ) . '" class="post-state-format post-format-icon post-format-' . $format . '" title="' . $label . '">' . $label . ":</a> ";
+					}
 				}
 
 				if ( $can_edit_post && $post->post_status != 'trash' ) {