Friday's violence took place at the Agricultural Penitentiary of Monte Cristo, in Brazil's Roraima state in the Amazon, according to Roraima state authorities. The prison is the largest in the state.
The rioting began early Friday and military police officers entered the prison to bring the situation under control, state authorities said.
In October, 25 people were killed in another riot at the same prison.
Sunday, nearly 60 prisoners were killed during a 17-hour uprising at the Anisio Jobim Prison Complex
in the city of Manaus, in the neighboring state of Amazonas.
The violence on New Year's Day was between incarcerated members of two gangs: the Familia do Norte (FDN) and the Primeiro Comando da Capital (PCC).
Brazilian Justice Minister Alexandre de Moraes said he doesn't believe the riot at the Monte Cristo prison was in retaliation for last weekend's incident.
All the inmates in Friday's violence were from one gang -- the PCC -- who were already separated from rival gangs, Moraes said at a news conference in Brasilia.
He spoke at a presentation of the government's new National Security Plan, which he officially launched Thursday with Brazilian President Michel Temer.
Moraes said nearly 50% of the prison population in Brazil is made up of "temporary prisoners" -- which includes those awaiting trial and those who have not yet been convicted. Moraes said he hopes to reduce that number to 18% under the new plan.
"We need a more rational prison system in Brazil. Our current system, by no fault of anyone specifically, arrests many people but not always the right people," Moraes said. "We have a lot of prisoners who should not be in jail."
Brazil has the fourth largest prison population in the world, with more than 622,000 people behind bars, according to its justice ministry. That puts it behind the United States, Russia and China.