I believe something like the following should get you close to where you want to be.

Given this directory structure:

orig
  |-a
     |- a.txt
  |-b
    |- b.txt
  |-c
    |- c.txt
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...and running this code:

use strict;
use warnings;

use Archive::Zip;
use File::Basename;
use File::Copy::Recursive;
use File::Find::Rule;

use constant AZ_OK => 0;

my $mkvingestdir = 'orig';
my $mkvingestdest = 'new';
my $zip_dest = 'zipped';

File::Copy::Recursive::dircopy $mkvingestdir, $mkvingestdest 
    or die "copy failed: $!\n";

my @dirs = File::Find::Rule->directory()
                           ->in($mkvingestdest);


for my $dir (@dirs){
    next if $dir =~ /(?:\.|\.\.)/;
    next if $dir eq $mkvingestdest;

    my $zip = Archive::Zip->new;
    $zip->addDirectory($dir);

    my $name = basename $dir;

    if ($zip->writeToFileNamed("$zip_dest/${name}.zip") != AZ_OK){
        print "error in archive creation\n";
        next;
    }
    print "archive created successfully\n";
}
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I get the following zip files in the zipped zip destination directory:

$ ls zipped/
a.zip  b.zip  c.zip
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