Claims that the placenta contains vitamins which could benefit a woman's health have increased interest in the practice in recent years.
But a review by Northwestern University found no proven benefits and no research on the potential risks.
The Royal College of Midwives said it should be the woman's choice.
The researchers said the popularity of eating placentas had risen in the last few years but this may have been due to women being influenced by media reports, blogs and websites.
Their review, published in Archives of Women's Mental Health, looked at 10 published studies related to placenta eating.
But it could not find any data to support the claims that eating the placenta raw, cooked or in pill form carried any health benefits.
Placentophagy, as the act of eating placentas is known, has been said to reduce pain after delivery, increase energy levels, help with breastmilk production and enhance  bonding between mother and child.
Some are also convinced that it replenishes iron stores in the body, but the research team said this was based on subjective reports rather than scientific research.
The review also said there were no studies which looked at the risks of eating the placenta.
The organ acts as a filter to absorb and protect the developing foetus from toxins and pollutants.
As a result, the scientists said, bacteria or viruses could remain within the placenta tissues after birth.
Lead study author Cynthia Coyle, a clinical psychologist at Northwestern University, said: "Our sense is that women choosing placentophagy, who may otherwise be very careful about what they are putting into their bodies during pregnancy and nursing, are willing to ingest something without evidence of its benefits and, more importantly, of its potential risks to themselves and their nursing infants.
"There are no regulations as to how the placenta is stored and prepared, and the dosing is inconsistent.
"Women really don't know what they are ingesting."
Louise Silverton, of the Royal College of Midwives, said there was not enough evidence for them to be able to advise women about eating their placenta.
"It must be the woman's choice if she chooses to do so.
"Women should be aware that like any foodstuff, placentas can go off, so care will be needed about how they are stored."
She added: "If woman is intending to do this, they should discuss it with their midwife ahead of the birth so that arrangements can be made to ensure she gets her placenta."
Dr Daghni Rajasingam, spokesman for the Royal College of Obstetricians and Gynaecologists, said although the placenta is very rich in blood flow, there were potential risks to ingesting it.
"What women do with their placenta is up to them - but I wouldn't recommend they eat it."
There is no scientific evidence that eating the placenta after childbirth can protect women against depression and boost energy, US research suggests.