It appears blazar has the best approach. I added data validation to, and bencmarked, the two main solutions (regexes and unpack), as well as doing the same thing with sprintf (just for fun).

@my_array = <DATA>;

use Benchmark ':all';


sub regex_method {
    my  $array = [@_];
    for (@$array) {
        next unless /^\d{6}\s*$/;  ## validate data
        s:(\d{2})(?!$):$1/:g;
    }
}

sub sprint_method {
    my $array = [@_];
    for (@$array) {
       next unless /^\d{6}\s*$/;  ## validate data
       $_ = sprintf "%d%d/%d%d/%d%d", split('',$_);
    }
}

sub unpack_method {
    my $array = [@_];
    for (@$array) {
        next unless /^\d{6}\s*$/;  ## validate data
        $_=join '/', unpack 'A2' x 3, $_ for @arr;
    }
}

cmpthese( 50000, {
    'regex'   => sub { regex_method(@my_array) },
    'sprintf' => sub { sprint_method(@my_array) },
    'unpack'  => sub { unpack_method(@my_array) },
});

__DATA__
010203
020304
012398
122399
[download]

With these results (representative of many runs):

           Rate sprintf   regex  unpack
sprintf 20383/s      --    -23%    -79%
regex   26441/s     30%      --    -73%
unpack  96899/s    375%    266%      --
[download]