Is there a Japan based "Open University" (correspondence) type of university where I could study Japanese?

Question:

And get a degree? (I live in India)

Answer:

This is one correspondence university in Japan.
http://www.ouj.ac.jp/eng/index.html

BTW, Japanese universities are not places where you study Japanese. It's for students who already have enough proficiency in Japanese and want to study something else.

If you want to study Japanese, you have to go to a Japanese language school.