What kind of "medical degree"? Med technician? Nursing? Doctor of surgery? Radiological tech?
There is work on the U.S. military bases, of course, under SOFA status, but if you want to work in Japanese hospitals or clinics, you're going to need licensing from Japan and a very strong command of Japanese.
Did you miss the part about needing to pass the national licensing exam in Japanese?
Seriously, of how much use do you think you would be dealing with Japanese patients when you can't speak Japanese? Or doing paperwork in Japanese?
And a "medical degree" is generally construed by most people as the degree one takes to become an M.D. There's no such thing as a phlebotomist in Japan; you would need to be a nurse or a physician in order to draw blood.
You don't know Japanese, yet you want to work in a Japanese hospital/clinic. Uh, think in reverse. If someone wanted to be a med assistant in your own country but couldn't speak, read, or write the language, what do you think would be the odds of landing such a job?
As I wrote before, if you are dead set on coming to do that line of work, seek out the American military bases.
There are no doubt many countries in the world with underdeveloped medical systems which are glad of any help they can get from anywhere and don't place too terribly many conditions or barriers in the way. Japan, however, is not one of them. If anything, the system could in some instances be considered overdeveloped and bloated. Not in all ways and all cases, but enough that with very limited exceptions Japan doesn't look to outsiders to fill positions.
If you are linguistically competent, have the requisite education, can pass licensing exams in Japanese, and wrangle a visa then you conceivably could compete for a job. But unless you're the next Albert Schweitzer, you could expect to lose out to practically any Japanese person who also applied for the same spot.