早稲田 is "preferably 3 years or equivalent experience"
http://www.waseda.jp/wbs/mba_fulltime/admission.html
慶応 doesn't have any prerequisite in terms of work experience.
KBS MBA Application - Keio Business School
They are the top 2 private universities.
早稲田 offers a course taught in English. I don't know if it's worth going there just to take English classes though. And you'll probably need to study about 2000 hours to be admitted to the course taught in Japanese. If I were you, I'd find a collage that offers exchange program with Japanese universities in the states and study Japanese before going there. Japanese is a lot harder than French or any European language, it takes 4 times the time you would spend on French to get to a certain skill level. Going to a language school doesn't cut it unless you are planning to spend 2 to 3 years full time there.
Edit: The word MBA instantly made me assume you lived in the states. What's your mother tongue? You'd need a lot less if you speak, say Chinese or Korean. Expect to get JLPT1 though, which would take about 900 hours for a Chinese guy.