There are numerous ways to do what you want, ranging from the nice threads example by BrowserUk, to using "fork-and-exec" in a subroutine. The easiest way is to use the non-blocking Tk::ExecuteCommand module. Here are 2 simple examples, one spawns a new toplevel for the command.

#!/usr/bin/perl -w
use Tk;
use Tk::ExecuteCommand;
use Tk::widgets qw/LabEntry/;
use strict;

my $mw = MainWindow->new;

my $ec = $mw->ExecuteCommand(
    -command    => '',
    -entryWidth => 50,
    -height     => 10,
    -label      => '',
    -text       => 'Execute',
                            )->pack;
$ec->configure(-command => 'date; sleep 10; date');


my $button = $mw->Button(
            -text =>'Do_it',
            -background =>'hotpink',
            -command => sub{ $ec->execute_command },
                        )->pack;

MainLoop;
[download]

and if you want separate windows, try something like this:

#!/usr/bin/perl -w
use Tk;
use Tk::ExecuteCommand;
use Tk::widgets qw/LabEntry/;
use strict;

my $mw = MainWindow->new;

my $top = $mw->Toplevel;
$top->withdraw;

my $ec = $top->ExecuteCommand(
    -command    => '',
    -entryWidth => 50,
    -height     => 10,
    -label      => '',
    -text       => 'Execute',
                             )->pack;
$ec->configure(-command => 'date; sleep 10; date');


my $button = $mw->Button(
             -text =>'Do_it',
             -background =>'hotpink',
             -command => sub{
                  $top->deiconify;
                  $top->raise;
                  $ec->execute_command;
                  $top->withdraw
                      },
                        )->pack;

MainLoop;
[download]