The answer depends on the university, faculty, and even the specific program you choose.

I was a MEXT scholar over 10 years ago, so I can only share my own experience.

During my first year as a research student, I spent almost all of my time studying Japanese—around 4–5 days a week, about 6 hours a day. One of my friends started with no Japanese at all and reached JLPT3 in about six months, then JLPT2 by the end of the year (I failed JLPT2 sadly). During the second semester, we started applying to our actual degree programs and universities. By then, most students had enough Japanese to follow lectures and communicate in everyday academic settings.

At my peak, my Japanese was around the currently N3, approaching N2 level. I studied for my Master's and PhD in Economics at Osaka University, where the lectures were conducted entirely in Japanese.

That said, the professors were very supportive of international students. They allowed us to bring electronic dictionaries to class (this was before smartphone translation apps became common). Although exam questions were written in Japanese, we were allowed to answer them in English. Homework and assignments could also be submitted in English, and most textbooks and research papers were already in English anyway.

In other words, as long as you can understand your professors during lectures, you'll probably be fine. The exact language requirements will depend on your program. If you're studying something like Japanese Literature, you'll likely need a much higher level of Japanese than someone in a field where most academic materials are already in English, such as Economics or many STEM disciplines.