Here is one way, manipulate the options array. 
#!/usr/bin/perl
use warnings;
use strict;
use Tk;

my @hrs = ("1", "2", "3", "4", "5", "6",
"7", "8", "9", "10", "11", "12");

my $mw = new MainWindow();
my $menu = $mw->Optionmenu( 
           -options => \@hrs,  
       -textvariable => \$hrs[0] )->pack();

$mw->Button(-text=>'Shift',-command => sub{
      push (@hrs, shift(@hrs));
      $menu->configure(-options => \@hrs, -textvariable => \$hrs[0] );
      $mw->update;
    })->pack();

#start up at desired value
my $desired = 3;
push (@hrs, shift(@hrs)) until $hrs[0] == 3;
$menu->configure(-options => \@hrs, -textvariable => \$hrs[0] );

MainLoop;

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In reply to Re: Tk Optionmenu - how to set the default selection by zentara
in thread Tk Optionmenu - how to set the default selection by Minok

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