#!/usr/bin/perl
use strict;
use warnings;
use Archive::Zip qw(:ERROR_CODES :CONSTANTS);

my $filename = "XXXXXXXXXXXx.zip";   
my $zip = Archive::Zip->new();
unless ($zip->read($filename) == AZ_OK) {
    die "Read error\n";
}
my @members = $zip->members();
foreach (@members)
{

     #Try to use any of the following function
     #unless ($_->compressedSize())
            (OR)
     #unless($_->uncompressedSize()) 
     
}
[download]

Loop through the members, use compressedSize() or uncompressedSize() function to find the file size is zero and do what you want in if condition.