Praise be to Allah.
We put the following question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen:
What is the ruling on keeping the placenta to treat cancer and remove facial wrinkles?
He replied as follows:
It seems that there is nothing wrong with it so long as there is proof that it is an effective treatment.
Question: does the rule that whatever is taken from a living being is dead apply in this case?
Answer: dead matter of human origin is taahir (pure).
Question: and if it is of no use, should it be buried, or can it be disposed of in any place?
Answer: it seems that it is the same as nails and hair.
And Allaah knows best.