You have to add your subarrays by reference. Here's one way:

 push @masterarray, \@subarray;

If, by chance, you'll be reusing @subarray repeatedly, you may want to push a reference to an anonymous copy of it instead so that the original is preserved. You can do that like this:

 push @masterarray, [@subarray];

You should have a look at perlreftut, perllol, and perlref. The first of those three documents is a tutorial on references. The second is a sort of cookbook for manipulating "lists of lists" or "arrays of arrays". And the third is an in depth discussion of references. All very helpful. If you plan to use Perl more than once in your life, it will pay to spend an hour or so reading those three docs.