Most likely not (however it is always good to have)
The Japanese Immigration Bureau regulations about acceptance into the country on short-term visas are, that you need to show proof that you have a plan to leave / funds to do so before the end of your visa if requested.
Referring to the MOJ-IMMI website, you will notice that the rule is not specifically stated outright, but is instead enshrined as one of the possible reasons of you "not meeting landing permission requirements" (of which the law is also intentionally vague about).
Another factor you may have with having to present proof of a return flight, is which country you are a citizen of. For example, although generally untrustworthy with matters of Immigration, various sources (for example; the Embassy of Japan in the UK, the UK government and the Embassy of Japan in Malawi) state that for your Visa, a return ticket may / is required.
Feel free to take it as you will. You are likely fine most of the time, however, if the Immigration Official insists on checking, you may want to have some kind of proof (money, credit card, return ticket etc.) lest you face rejection at the border.