Based on your code, but made recursive, and with less array references:

#!/usr/bin/perl -w
use strict;

sub foo { print "FOO!\n" }
sub bar { print "BAR!\n" }

sub menu {
    my ($menu) = @_;
    for (;;) {
        print "\n$menu->[0]\n";
        print map "$_. $menu->[$_ * 2 - 1]\n", 1 .. $#$menu / 2;
        print '> ';
        chomp (my $choice = readline *STDIN);
        if ($choice and $choice <= $#$menu / 2) {
            my $action = \$menu->[$choice * 2];
            return if not defined $action;
            $action->()  if ref $action eq 'CODE';
            menu $action if ref $action eq 'ARRAY'
        } else {
            print "Invalid choice: $choice\n"
        }
    }
}

my ($mainmenu, $submenu);

$mainmenu = [
    'Main menu',
    'Foo'        => \&foo,
    'Submenu...' => sub { menu $submenu },
    'Exit'       => undef,
];

$submenu = [
    'Submenu',
    'Bar',                  => \&bar,
    'Back to previous menu' => undef,
];

menu $mainmenu;
[download]

menu [
    'Main menu',
    'Foo'        => \&foo,
    'Submenu...' => [
        'Submenu',
        'Bar',                  => \&bar,
        'Back to previous menu' => undef,
    ],
    'Exit'       => undef,
];
[download]

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