It is not currently known but there are approximately 424 golf courses in Japan so there must be quite a few.
AnswerThat's nowhere near right. There are over 2300 golf courses in Japan. During Japan's bubble economy in the 1980's literally hundreds of courses were built.
Numbers of golfers in Japan:
I've seen some market research data that puts the number at about 12 million. Recently, the emergence of young talents like Ryo Ishikawa and Ai Miyasato has increased the sports popularity with the younger generations and also female golfers.
Two good sources about Golf in Japan (in English):