"A fight began between rival groups of inmates, resulting in fatalities," a spokesman for the justice secretary said. Guards had retaken control of the facility, he said.
The bloodshed took place in the Itapaje Public Prison, about 78 miles (125 km) from the state capital Fortaleza.
On Saturday, at least 14 people were gunned down at a nightclub in Fortaleza. Local media reported that the massacre, conducted by armed men who arrived in three cars, was related to disputes between rival drug traffickers.
Last year there were a record 5,114 murders in the state of Ceara, a 50 percent rise from 2016.
Brazilian prisons are notoriously overcrowded, with 726,712 inmates as of June 2016 and capacity for only 368,000, according to the most recent official statistics.
The country is also one of the most violent in the world, with nearly 60,000 homicides annually. A year ago, 56 were killed in an uprising in a prison in the city of Manaus in Brazil's Amazon.