In all my years here I have never seen or even heard of a foreign doctor in Hokkaido. I believe there may be a few in big cities like Tokyo and Osaka with their own practices who almost solely see foreign patients. As I said earlier I doubt very much that any public hospital would hire a foreign doctor. I just don't think it ever happens. Anyone ever seen a foreign doctor in a hospital here?
As Nyororin points out you would need to pass exams for a licence to practice medicine in Japan which would mean you'd require fluency in reading and writing as well as speaking. Not an easy task to get that fluent if you're also studying medicine!
There are some in government though who want to make it easier for foreign doctors to practice here. Still knowing the beauracracy here give it another 10-15 years or so before anything actually changes
Minister wants top-level foreign doctors to provide medical care in Japan