Japanese level for graduate studies
I t sounds like you may be in one of the azia jinzai programs. But in any case, if you are doing a masters program in Japanese (fully in Japanese, you should be well ABOVE JLPT lvl 2). However, most programs that accept foreign students make consider the language issues that the students are encountering.
If you are in one of the azia jinzai programs, you need to reach JLPT lvl 2 for graduation. If you are in a program that is taught in English, then you need survival Japanese (JLPT lvl 3 is fine). If you are in a research program, you will be able to manage with JPLT 3, since much of your learning will involve reading academic papers (in English), self directed research, and interaction with prof (who will most certainly speak English) and students (who may or may not).
Hope that helps