Don't know how to do this in Perl CGI, but the general idea that I've seen implemented is this:

1. When loading the form, generate some unique sequence number and include it in a hidden field of some sort
2. When pressing Submit, have it call a client-side Javascript function that, before submitting the form, pops up another little window, pointing to a different CGI script and using this unique number as one of the parameters
3. The upload script then begins processing, regularly storing its progress in some sort of session variable tied to the unique number
4. The CGI feeding the popup checks the status and generates HTML simulating a progress bar, with an appropriate refresh interval
5. Once the file is done, the CGI feeding the popup will detect this and in its HTML output include a line like <script>window.close()</script> or some such.

It's kind of crude, and it definitely relies on client-side Javascript, but it works. Other posts in this thread have suggested how to track the progress of an upload on the server side (needed for step 3).

Update: This solution will probably require mod_perl or something else that allows two scripts to share server-side information