japhy's code is certainly very quick, Benchmarking about 43% better than anything I could come up with on short notice. The 'radix_sort' is obviously more efficient for this kind of application than the built in sort of Perl.

However, under Perl 5.6 + strict + '-w', the following change is required to avoid compilation errors:

  sub IPsort {
    map inet_ntoa($_),
    IP_radix_sort
    map inet_aton($_),
    @_;
  }
[download]

The alternative code which Benchmarks in at #2, but has the advantage of simplicity:

    sub byip { inet_ntoa($a) cmp inet_ntoa($b) }

    foreach (sort byip @ip_list) ...
[download]

BTW, I tested both with 100_000 random IP addresses by 10 runs (approx 86 to 150s per test).