I looks like I'm long scooped, but this was too much fun to hurry :-) Thanks for the super question!

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

sub zen
{
   my $coderef = shift; # the code ref is a
   &$coderef; # Find the inner meaning[s]
#   &$coderef;
};

my $petition = "How can I put a variable that is only visible to zen f
+rom within this anon code block?";

zen do {
    my $speech = $petition;
    print $speech,$/;
    sub {
        $_ = shift;
        $speech = $speech =~ /^How/ ?
            $_ :
            "Mu.";
        print $speech,$/;
    }
}, 
    "There is do and there is not do.";
[download]

Update: Replaced tabs to fix formatting.

After Compline,
Zaxo