If the string that marks the end of a zone block is really consistent and distinctive -- e.g. every block ends with a line whose first character is "}", and this is only found at the end of a block -- you can use the input record separator variable "$/" to make this much easier.

#!/usr/bin/perl

use strict;

( @ARGV == 2 and -f $ARGV[0] )
    or die "Usage: $0  input.file  domain.to.comment.out\n";

my ( $in_file, $rem_domain ) = @ARGV;
open IN, "<", $in_file or die "$in_file: $!";
open OUT, ">", "$in_file.new" or die "$in_file.new: $!";

$/ = "\n}";     # input record separator is line-initial "}"

while (<IN>) {               # $_  contains a whole zone block
    if (/\W$rem_domain\W/) {
        s/^/#/;              # add initial comment to block
        s/\n/\n#/g;          # add comment after each "\n"
    }
    print OUT;
}
[download]

The number of zone blocks that will be commented out in the file depends on what the user provides as the second command line arg on the script. I would recommend that you not rename the output to replace the input file as part of this script: the user should have a chance to confirm that the output file was changed as intended -- e.g. that there wasn't a mistake in the second command line arg.

(It could happen that someone hits the "Enter" key too soon, and comments all zone blocks that match an unintended substring.) BTW, this approach is also an easy way to uncomment a chosen block, in case you ever need that sort of tool.

(update: forgot mention: look up $/ in perlvar)