I'm not sure what you have in mind by "moral harm" but one thought would be that moral harm to someone results when a moral obligation to that person is violated. So if I have a moral obligation to respect your bodily integrity, then if I assault you, I violate that obligation and not only cause you pain and suffering, but moral harm.

If this is the idea, then the question really turns on whether we have moral obligations to ourselves. It seems plausible that we do. One might argue that just as it would be wrong for another to violate my bodily integrity, it would be wrong for me to do so as well, e.g., by chopping off my own hand. Here it might be worth asking: if I am morally entitled to a certain kind of treatment, e.g., say that there is a moral requirement that persons be treated with respect, can I ever legitimately exempt myself from the rule, even when my action is directed towards myself? If not, then it seems one can morally harm onself by not according oneself due respect.