my @ips = qw(   127.0.0.1
                0.0.0.0
                256.0.0.1
                123.555.333.222666  );

foreach my $ip (@ips) {
    my $f = undef;
    if($ip =~ m/^(?!0+\.0+\.0+\.0)
                ([01]?\d\d?|2[0-4]\d|25[0-5])
                \.([01]?\d\d?|2[0-4]\d|25[0-5])
                \.([01]?\d\d?|2[0-4]\d|25[0-5])
                \.([01]?\d\d?|2[0-4]\d|25[0-5])$/x ) {
        $f =1;
    }
    print 'Is', $f ? "" : 'n\'t', " valid and/or usable IP: $ip \n"
}
[download]

Is valid and/or usable IP: 127.0.0.1 
Isn't valid and/or usable IP: 0.0.0.0 
Isn't valid and/or usable IP: 256.0.0.1 
Isn't valid and/or usable IP: 123.555.333.222666
[download]

It doesn't check for range, so you can do:

use Data::Validate::IP qw(is_ipv4);

my $ip_w_mask = '10.3.2.0/28';

my ($ip, $mask) = m{^(.*)/(\d+)$}
   or die("Incorrect format: Mask not found\n");

is_ipv4($ip)
   or die("Incorrect format: Malformed IP address\n");
[download]

A relatively simple (and too permissive) regex would be:

if ($qs =~ /^[a-zA-Z0-9][a-zA-Z0-9\.\-_]*(\/\d+)?$/) {
  # do stuff with $qs
}
[download]