Although I live in Kyoto, both Kobe and Osaka are only around 90 minutes away by train. The other day I went to visit Kobe Mosque, one of the oldest mosques in Japan.
Muslims first arrived in Japan in the late 19th century, the first official contact was with the Ottoman Empire. Kobe 神戸can be translated as the 'gate of God', and it was the main gateway, along with Yokohama, into Japan for many foreigners, Muslims included. The first major group of Muslim emigrants to Japan were Kazan Russians, fleeing the Russian Revolution. They built Kobe Mosque in 1935. You can find a thorough history of the mosque here, http://www.kobemosque.org/History%20English.htm.
Today the Muslim community of Kobe is largely made up of South Asians who specialise in exporting second-hand cars, and foreign students. Looking around the mosque today, it's hard to imagine the kind of tight-knit community of Kazan Turks, Arabs, Indians and others that existed here in the 1920's and 30's. I'm not an expert or anything, but it seems to me that Muslim communities here don't tend to put down roots, they are here for strictly economic reasons, and when the economy changes, they move on.