push will also work without explicitly defining your sub-arrays and getting references to them, as in the following:

use strict;
use warnings;
use Data::Dumper;

my @letter_array = ();
my @letters = ('A' .. 'Z');

foreach my $letter (@letters) {
    my $selection = int rand 4;
    push @{$letter_array[$selection]}, $letter;
}

print Dumper(\@letter_array);
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Will produce (in at least one case):

$VAR1 = [
          [
            'F',
            'K',
            'O',
            'T',
            'U',
            'V',
            'X'
          ],
          [
            'B',
            'I',
            'Q',
            'W'
          ],
          [
            'A',
            'D',
            'E',
            'H',
            'J',
            'L',
            'M',
            'P',
            'S',
            'Z'
          ],
          [
            'C',
            'G',
            'N',
            'R',
            'Y'
          ]
        ];
[download]

This works because of autovivification. Check perlref in your docs if this fifty-pfenning term piques your interest.