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TL;DR: Yes, but the ways in which it could go wrong if done incorrectly mean it is essentially guaranteed to be deemed never worth the risk.
Microwaves don't heat food "from the inside" necessarily, but from a depth that the microwaves manage to penetrate into it. In the cases of the microwave frequencies used in domestic appliances, that translates to around 4cm, give or take a small amount. So you would theoretically be able to heat your subject subcutaneously down to that depth. Note that the surface would also get heated in the process. There are fancy formulae to determine what the graph looks like of energy imparted to water (for sake of argument) in what proportion at what depth, but I won't get into that here. This may or may not be useful for some manner of non-supervillian related purpose, but I can't think of what that might be off the top of my head.
If the question is, "does exposure to microwaves cause any kind of freaky health effects, cause cancer, or induce mutant superpowers over and above just heating up the subject," the answer insofar as we can determine is no.
However, it is absolutely possible to cause a wide array of boring old regular injuries up to an including death by, not to put too fine a point on it, cooking people. It's very easy to bring water and other liquids to a boil by heating via microwave, for instance, and doing that inside the subject's skin is probably a recipe for disaster. You would have to be able to accurately control the amount of energy imparted on the subject, and you would need some compelling reason why you'd have to do that via microwave versus innumerable more traditional methods many of which are inherently fail-safe, like just immersing them in warm water.
Your skin can (kinda sort of) sense temperature, but what about the muscle, fat and bone that sits below the skin? If those parts get suddenly heated up, would you even notice before it’s too late? If not, this could lead to some serious damage.