The 2001 rules of golf
stipulate that "the overall length of the club shall be at least 18 inches (457.2 mm) measured from the top of the grip
along the axis of the shaft or a straight line extension of it to the sole
of the club
The shorter your putter is (as long as you're not doing something vaguely resembling cheating like anchoring the butt end of the putter in your breastbone), the better off you are! Just as a shorter club is easier to hit, so a shorter putter is easier to stroke accurately!
I'm not very tall (5'8", full-grown). When I grip a typical made-for-the-average-american-male putter correctly, my hands are at least half off the bottom of the grip onto the metal. In trying to make a triangle with my arms and shoulders, my hands really do go that far down the putter. Not good. The metal is cold. It doesn't feel right. It shouldn't feel right! The average putter sold is made more for a 6' man than a 5'8" man.
Putters are not a one-size-fits-all proposition, just as golf clubs aren't either. The neat part is that the rules of golf allow you to make your putter very short, should you desire to do so. So, I lopped a couple inches off my putter, popped a new grip on it (I really like the Winn brand putter grips), and now my hands fit the grip correctly. Since shortening my putter, I believe that my distance control has improved, as has my accuracy. If you're short, you may want to consider it too.