Thank you for the suggestions! The GUI does remain reactive because I use $mw->update; while downloading the file in order to update a Progressbar.

I opted for a quite easy solution which shows a top window with a grab until the download process is completed.

    my $tl = $mw->Toplevel( -title => 'WAIT' );
    $tl->resizable( 0, 0 );
    $tl->transient($tl->Parent->toplevel);
    $tl->protocol('WM_DELETE_WINDOW' => sub {});   
    $tl->grab;
    my $image_file = "wait.jpg";
    my $splashphoto = $tl->{Photo} = $tl->Photo(-file => $image_file);
    $tl->Label(-image => $splashphoto, -bd => 0)->pack(-fill => 'both'
+, -expand => 1);
[download]