Plato mentions them in passing in his Republic, less in a way that implies an argument that women should be allowed to work as physicians than simply taking the fact that they already did so as a matter of course. Feminine forms of the Greek word were used widely enough and in such contexts as to make clear that these women were not merely midwives. I would argue, however, that given Athenian attitudes towards women and freedom of movement, it would be unsurprising if there were fewer female physicians there than elsewhere in Greece.*
Most female physicians probably attended primarily to women and so-called female problems, but they also concerned themselves with the broader practice of medicine. The civic honors granted to Antiochis in the 1st century CE argues she at least, probably had a wide variety of people with a wide variety of complaints as her patients. Other evidence can be gathered from the quotations of the works of female physicians found quoted by male authors, though it weights more towards later periods than early ones.
The information we have is scarce enough that we cannot know what social class these women might have belonged to or just how common or uncommon they were. All we can say for sure is that these women existed and that some of them, particularly but not only in later centuries, had enough training and enough prestige to be referred to as physicians, with the implication that this title was distinct from that of midwife.
*Though I will point out that this is pure guesswork.
Plato, Republic (464d, 455e) - Perseus
Inscription regarding Antiochis of Tlos (Pleket 12), found in Lefkowitz & Fant
Parker, Holt N. "Women physicians in Greece, Rome, and the Byzantine Empire." In Women Healers and Physicians: Climbing a Long Hill, edited by Lilian R. Furst, 131-150. University Press of Kentucky, 1997. [Note: can be found here on academia.edu]
Pomeroy, Sarah B. Goddesses, Whores, Wives, and Slaves. New York: Schocken, 1995.