Twenty Thirteen theme is responsive theme and  some excellent features.My blog is receiving lot queries in customization for Twenty thirteen theme.So I am writing this tips to disable search box icon from the menu bar header.

Remove Search Bar from Twenty Thirteen Theme

If you need to remove the search box from Twenty Thirteen theme, you need to edit header.php file.
Go to Dashboard  >>  Appearance  >> Editor select  header.php file from right side and comment following piece of code by adding “//” infront of the function get_search_form(); .

<?php get_search_form(); ?>
To
<?php //get_search_form(); ?>

Save the changes by clicking update file.
Now Search box is removed from Twenty Thirteen theme.