You need to provide -d with the $path ...

#!/usr/bin/perl -w

use strict;

my $path = "/usr/bin";

opendir DIR, $path or die "Couldn't read directory: $!";
    my @directories = grep { -d "$path/$_" } readdir DIR;
closedir DIR;

foreach (@directories) {
    print $_, "\n";
}
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Update: Changed $path to "$path/$_" so it prints out only the directories (as opposed to all the files). Thanks to ChemBoy for spotting this and providing the fix.