It's a fair question, but two issues:
(1) Traveller materials are super-sciency! You can build a spacecraft that can accelerate continuously at mulitple G's for days, and not have to worry about any micro-meteor fragments. So if the materials are that strong, you'd be able to put a nose cone on your missile that could do the same (weight and mass aren't factored into the mechanics).
(2) No interceptor-style missile mechanics are present in the game system. You'd have to introduce anti-missile missiles to get your fragmentation warheads into the game. That's not a bad thing (And long overdue, IMO), but it currently doesn't exist.
Whether or not a fragmentation burst would work is quite problematic. It gets back to the idea of material strength and it's ability to ignore damage. Just a few hits with fragments may be insufficient to destroy a missile.
You might want to go with mini-nukes to destroy or at least punch holes in large missile salvo's. The offset, of course, to that would be to spread your missiles in a much wider pattern so that there is no single concentration to destroy. And the cost of defense in Credits might bankrupt a navy.