Index: wp-admin/media.php
===================================================================
--- wp-admin/media.php	(revision 20420)
+++ wp-admin/media.php	(working copy)
@@ -106,7 +106,7 @@
 <h2>
 <?php
 echo esc_html( $title );
-if ( current_user_can( 'upload_files' ) ) { ?>
+if ( current_user_can( 'upload_files' ) && ! wp_is_mobile() ) { ?>
 	<a href="media-new.php" class="add-new-h2"><?php echo esc_html_x('Add New', 'file'); ?></a>
 <?php } ?>
 </h2>
Index: wp-admin/upload.php
===================================================================
--- wp-admin/upload.php	(revision 20420)
+++ wp-admin/upload.php	(working copy)
@@ -176,7 +176,12 @@
 
 <div class="wrap">
 <?php screen_icon(); ?>
-<h2><?php echo esc_html( $title ); ?> <a href="media-new.php" class="add-new-h2"><?php echo esc_html_x('Add New', 'file'); ?></a> <?php
+<h2>
+<?php
+echo esc_html( $title );
+if ( current_user_can( 'upload_files' ) && ! wp_is_mobile() ) { ?>
+	<a href="media-new.php" class="add-new-h2"><?php echo esc_html_x('Add New', 'file'); ?></a><?php
+}
 if ( ! empty( $_REQUEST['s'] ) )
 	printf( '<span class="subtitle">' . __('Search results for &#8220;%s&#8221;') . '</span>', get_search_query() ); ?>
 </h2>
Index: wp-includes/admin-bar.php
===================================================================
--- wp-includes/admin-bar.php	(revision 20420)
+++ wp-includes/admin-bar.php	(working copy)
@@ -489,7 +489,7 @@
 		unset( $cpts['post'] );
 	}
 
-	if ( current_user_can( 'upload_files' ) )
+	if ( current_user_can( 'upload_files' ) && ! wp_is_mobile() )
 		$actions[ 'media-new.php' ] = array( _x( 'Media', 'add new from admin bar' ), 'new-media' );
 
 	if ( current_user_can( 'manage_links' ) )