1. You create a list of IPs you find in @item;
2. You then pass them as a list into uniq_ip(@item)
3. Where you make a copy of that list my @list = @_;
4. You then make another copy when you pass it to map map { $_ => 1 } @list
5. Which you use to create an anonymous hash { map { $_ => 1 } @list }
6. Then you create another list from its uniq keys keys %{{ map { $_ => 1 } @list }}
7. Which you assign to an array my @uniq_ip = keys %{{ map { $_ => 1 } @list }};
8. Which is returned as another list (last statement of the subroutine).
9. Which you assign to another array @uniq_out = uniq_ip(@item);
10. Which you iterate over foreach(@uniq_out)

That makes 9 or 10 copies of the list. It's no wonder you're running out of memory.

Try this. It avoids most of those copies:

use strict;
use warnings;

open(OUTNOMATCH, ">nomatch.out") or die "Couldn't write to file $!";
open(OUTMATCH, ">match.out") or die "Couldn't write to file $!";

sub match_internal {  #Separate internal/external addresses

use Net::IP::Match::Regexp qw( create_iprange_regexp match_ip );

    my $my_ip = $_[0];
    my $regexp = create_iprange_regexp(
       qw( 192.168.0.0/16 10.10.0.0/16 192.3.3.0/23 192.168.24.0/21 10
+.0.0.0/8 )
    );
        if (match_ip($my_ip, $regexp)) {
            print OUTMATCH "$my_ip\n";
        }
        else {
            print OUTNOMATCH "$my_ip\n";
        }
}

sub sortme { # sort all addresses
    my @array = @_;
    my %hashTemp = map { $_ => 1 } @array;
    my @array_out = sort keys %hashTemp;
}

sub main_loop { #main loop that performs all logic and munging

    my %uniq;

    while (<>) {
        (my $field1, my $field2) = split /DST=/, $_;
            if ($field2 =~ m/(\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3})/) {
                $uniq{ $1 } = 1;
            }
    }
    match_internal( $_ ) while $_ = each %uniq;
}

main_loop();
[download]

You're also re-creating this:

    my $regexp = create_iprange_regexp(
       qw( 192.168.0.0/16 10.10.0.0/16 192.3.3.0/23 192.168.24.0/21 10
+.0.0.0/8 )
    );
[download]

for every uniq IP you check...which probably doesn't cost you in extra memory, but is hugely wasteful of cpu (time).