It's not a requirement, per se, but it's encouraged that you at least acquire a rudiment conversational understanding of the language. From my understanding, most language schools are quite lenient. You can easily get around Tokyo without understanding Japanese. Practically every sign, including public transport, will have an English translation. Of course, on a social level, speaking the language would also help, in addition to teaching. If you apply for the JET, it's less of a requirement to know Japanese because you'll be a teaching assistant, but it's a lot harder to gain acceptance to this program.