Answering the original question: the off-the-shelf answer a locksmith would give you is probably an electric strike or electric deadbolt, of the same sort used on doors.
A maker would probably suggest just using a spring-loaded solenoid directly as the latch. (That's what's going on inside the electric strike, though with some mechanical engineering wrapped around it for strength and reliability.)
If you want to control this from electronics rather than simple switches, you'll need a driver circuit appropriate for the solenoid. (Relay or equivalent plus a few components to make that friendly to the transistors. )
... I also highly recommend the Tot Locks (currently sold by Safety 1st, I think) . That's a magnet-operated latch, sold for childproofing but useful for other purposes too. It's just plastic so it can be forced, but it's strong enough to keep kids out until they're old enough to understand magnets and action-at-a-distance, and strong enough to constitute a Very Strong Suggestion to your nosy relatives that they aren't supposed to open this cabinet or drawer.
(I was giving these out as baby-shower gifts for a while, having been able to pick up a case ar below-wholesale price. Universal reaction was that these were the only latch that held up to determined and clever toddlers.)
No connection with the product, just a happy user.