Anybody involved in female genital mutilation (FGM) would be punished with a fine and imprisonment, it said.
The move follows a campaign against the practice by the National Union of Eritrean Women, which says more than 90% of Eritrean women are circumcised.
FGM typically involves removing the clitoris and FGM supporters argue that it helps prevent promiscuous behaviour.
The practice is widespread in many parts of Africa and the Middle East.
Women carry out the surgery as part of an initiation rite to adulthood.
It is known to be a very painful practice that sometimes leads to excessive bleeding, infection, trauma and difficulties in childbirth.
"Female circumcision is a procedure that seriously endangers the health of women, causes them considerable pain and suffering besides threatening their lives," the government proclamation said.
"Whosoever requests, incites or promotes female circumcision by providing tools or any other means and whosoever, knowing that female circumcision is to take place or has taken place, fails without good cause, to warn or inform the proper authorities promptly, shall be punishable with a fine and imprisonment," it continued.
The ban came into force on 31 March, the information ministry said.
FGM is outlawed in a number of African countries, but laws are rarely enforced.
