Q. There is an ancient (non-Jewish) tradition which has become popular among new moms, placenta ingestion. Moms report that they have less post postpartum depression, increased energy and milk production. Is a human placenta kosher, what about the placenta of kosher animals?

A. Placentophagia or the act of mammals eating the placenta of their young after childbirth, when done by humans, besides kashrus concerns, also presents health issues, as it could become easily contaminated by the lack of refrigeration and septic concerns. (See; Risks of eating the placenta at parents.com). The benefits are also questionable. (See; Should I eat my placenta, at webmd.com).
In regards to the kashrus of the afterbirth or shilya, if it was delivered by a kosher live animal that gave birth, it would be prohibited as being; yotze min hachai or a derivative from a live animal . (Chulin 77a, Rambam – Macholos Asuros 5: 13, Kaf Hachaim Y.D. 81 34). If the animal underwent proper shechita and the placenta was found inside, it would be permitted.
In regards to a human placenta, Rema (Y.D. 79: 1) rules like Rambam that, “It is Biblically forbidden to eat human flesh.” Although many Poskim adopt Rema’s strict ruling, some others maintain that the matter is unresolved or even rule like the Rishonim who are Biblically lenient, but still Rabbinically prohibited (see Taz YD 79:3, Pri Hadash 79:6, and Darkei Teshuvah 79:15).
Therefore, Horav Shlomo Miller’s Shlit’a opinion is to avoid human placentophalagia.
(Interestingly, the Torah mentions placentophalagia as part of the curses of the tochacha. Devarim 28: 57).

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a