Overriding the search block module output to add a custom wrapper
Put search-block-form.tpl.php into your theme directory, and modify it as you wish.

Another way is using hook_form_FORM_ID_alter().

/**
 * Implements hook_form_FORM_ID_alter().
 */
function HOOK_form_search_block_form_alter(&amp;$form, &amp;$form_state) {
  $form['#prefix'] = '&lt;div class="custom-wrapper"&gt;';
  $form['#suffix'] = '&lt;/div&gt;';
}