Short answer
Eating the placenta, raw, cooked or in capsules, is not allowed in the Hanafi school, because it is part of a human body and is impure. Burying it is the respectful way where possible; if the hospital disposes of it, there is no sin on you. Donating it, or cord blood, for medical treatment is a separate question and is allowed by many scholars.
Human parts may not be eaten or used for benefit out of the honour Allah gave the human being, and the placenta also carries impure blood. It is best wrapped and buried. Placenta pills, smoothies or remedies are not permitted.
The four schools agree on this.
Explanation
Some birth plans now offer placenta encapsulation, where the placenta is dried and put into capsules, or eaten raw in smoothies, with claims that it helps recovery and mood. Others keep it for "lotus birth" or plant it under a tree.
Eating it. Allah has honoured the children of Adam, and the Hanafi texts say that no part of a human may be sold or used for benefit for that reason, the same principle behind the rulings on human hair and milk sold as a commodity. The placenta is also soaked in blood, which is impure. So eating it in any form is not permitted. The health claims are not well proven, and you can ask your midwife or doctor about safer support for recovery.
Burying it. The scholars teach that parts separated from the body, even hair and nails, are buried rather than thrown into dirty places. Many Muslim families ask the hospital to give them the placenta and bury it in the garden or a graveyard, without any prayer or ritual. If the hospital needs it for tests, or will only dispose of it themselves, you have done nothing wrong.
Medical donation. Cord blood and placental tissue can be donated or banked for treating diseases such as leukaemia. Many scholars allow this with the parents' consent, because it serves life. See stem cells and cord blood.
Follow a qualified doctor or midwife on the medical side of the birth, and ask a mufti if you are offered something not covered here.
Ask a mufti about your own case. This answer explains the general ruling. When the details of your situation matter, as they do here, ask a qualified mufti and give them the full facts. Where to ask a scholar.
The evidence
Quran, Surah Al-Israa 17:70
۞ وَلَقَدْ كَرَّمْنَا بَنِىٓ ءَادَمَ وَحَمَلْنَٰهُمْ فِى ٱلْبَرِّ وَٱلْبَحْرِ وَرَزَقْنَٰهُم مِّنَ ٱلطَّيِّبَٰتِ وَفَضَّلْنَٰهُمْ عَلَىٰ كَثِيرٍۢ مِّمَّنْ خَلَقْنَا تَفْضِيلًۭا ﴿٧٠﴾
And We have certainly honored the children of Adam and carried them on the land and sea and provided for them of the good things and preferred them over much of what We have created, with [definite] preference.
The honour of the human being extends to the parts of the body.
Sunan Abi Dawud 3207
Graded sahih... كسر عظم الميت ككسره حيا ...
"Breaking the bone of a dead person is like breaking it while he is alive."
Human parts keep their sanctity and are not treated as material.
Where the ruling is recorded
- al-Hidaya, Kitab al-Buyu, Bab al-Bay al-Fasid. Selling or using human hair is not allowed, because the human being is honoured and none of his parts may be treated as property.
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, on hair, nails and human parts. Parts separated from a human are buried.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.