What is a good word for a person who doesn't masturbate?

Aonanist. An onanist being a man who masturbates or practices coitus interruptus, an aonanist would be someone who doesn't (similar to social/asocial).

I don't think onanophobe is right because that would indicate a fear of onanism while there are certainly other reasons for not practicing it.

You could call such a person an onanophobe.

asexual --> an-onanist?

Which is to say, I do not know either, but other people are attempting to coin a word that is the opposite of an onanist--a man guilty of the sin of onanism, or spilling his seed. This is an allusion to Onan, in Genesis 38:

Gen 38:8-10 (NRSV)

Then Judah said to Onan, ‘Go in to your brother’s wife and perform the duty of a brother-in-law to her; raise up offspring for your brother.’ But since Onan knew that the offspring would not be his, he spilled his semen on the ground whenever he went in to his brother’s wife, so that he would not give offspring to his brother. What he did was displeasing in the sight of the Lord, and he put him to death also.

While Ronald's aversion to onanophobe is well reasoned, it does have the benefit of a literary reference.

I have nothing to offer that refers specifically to masturbation, but you probably could accommodate (though you don't mention the context for your need) by using the adjective continent, which means “exercising self-restraint, especially sexually”.