If http://www.perltk.org/ptknews/5390.htm is to be believed, then it's as simple as,

$top->Busy;
call_you_sub_here();
$top->Unbusy;
[download]

I haven't tested it however, so YMMV

Update: Tested with ActiveState 5.8.3 and the default Tk, and it works for me.

use Tk;
my $mw = MainWindow->new;
$mw->Button(-text => "Goodbye World!", -command =>sub{exit})->pack;
$mw->Button(-text => "Act busy!",
            -command =>sub{$mw->Busy; sleep 1;$mw->Unbusy;})
   ->pack;
MainLoop;
[download]