You have to return array references instead

use Data::Dumper;

sub function {
   my @arr_a = (1, 2, 3);
   my @arr_b = (4, 5, 6);

   return (\@arr_a, \@arr_b);
}

my ($arr_a, $arr_b) = function();
print Dumper $arr_a, $arr_b;

__END__
$VAR1 = [
          1,
          2,
          3
        ];
$VAR2 = [
          4,
          5,
          6
        ];
[download]