I'm sure there's a proper way to disable it by code, but you could also do it dirty and simply change the CSS for that particular button to hide it.
It is an <input> with the class "epi-cmsButton-tools epi-cmsButton-Search".
For CMS 6 R2, The style for this is defined in C:\Program Files (x86)\EPiServer\CMS\6.1.379.0\Application\App_Themes\Default\Styles\ToolButton.css (line 322).
Add "display:none" for this element and its parent for a quick solution.
BEWARE that this is a CSS file used globally for all CMS 6 sites on that same server. If you only want to change it for your site, override the button's style in your own style sheet.
You'll find some tips on that in Arve's blogpost.
Thanks for the dirty trick :)
I guess I'm going to use this if I don't get any other information on how to disable the search button.
Is it possible to disable the search-button in the file manager? If yes, how can I do this?