After a counter (which 種類 is), も has a meaning of "as many as" (as in, "Oh, as many as that?") with an affirmative verb, or "not even" with a negative verb. Compare だけ which, in this sense, means "only" with an affirmative verb and "as many as" with a negative verb.
"In Japan, there are as many as about 15 types of headache medicine that don't require a prescription."
It seems a bit weird in English, because we wouldn't normally combine "as many as" with "about", but I guess combining も and 約 works in Japanese. But the nuance is the same - it's basically saying this number is higher than one might have expected.