The Aztecs had a large and establish pharmacopeia and a recognized class of ticiti (physicians). A ticitl could range from an elder who had some knowledge of healing practices to a more professional role. The practice of medicine in Mesoamerica, like in all pre-modern societies (and modern societies as well, if we're honest), was intrinsically tied up in magical practices. A ticitl was healer, but also a diviner, and those two acts were not seen as oppositional or even distinct.

Midwives hold a special place of distinction among the ticiti and are written extensively about in Sahagun's History of the Things of New Spain, which includes the description of a number of pre-, peri-, and post-natal care such as diet recommendations; advice on sexual activity; fetal manipulation akin to Leopold Maneuvers; "women's medicine" which is implied to include abortifacients and induction drugs; and even surgical abortion in the case of fetal death.

There are a few key texts which give insight into the healthcare of the Aztecs. Sahagun has a laundry list of various plants and other items used for medicinal purposes, though sometimes he just says something like "this was used as medicine" without going into details about the conditions a particular item treated or how. Other parts of his work are more descriptive of particular treatments for particular conditions. The Badianus Manuscript is a bit more straightforward text on remedies, listing conditions and then giving cures for each. Written in 1552, the work is also notable for showing how Mesoamerican and European medical practices were being integrated at the time. Another significant source are the writings of the Spanish Court Physician, Francisco Hernandez, who spent years cataloging the botanicals of Mesoamerica and, in proper colonial style, railing about how the ticiti did not follow the strict Galenic traditions upon which he had been trained.

Apologies for the stub of an answer, but you can read more a few more details in my previous comment on How advanced was medicine in Mesoamerica's Postclassic era? as well as in the question How did native american scientific knowledge affect european science upon the discovery (and further exploration) of America?, which deals more with the clash of intellectual cultures and Hernandez, in particular.