Inmates had earlier burned mattresses on the roofs of the prison's cell blocks, which house about 1,200 inmates, as hundreds of troops and federal police in riot gear moved in with tear gas, monitored by police helicopters, Reuters reported.
A key question is whether there is a link between the violence in the prison and ongoing violence in the city itself, our correspondent said.
Some reports said the rival gangs worked for the local "Azteca" drug gang, that in turn works for the Juarez drugs cartel.
Gonzalez said the authorities are investigating why the rival gangs were in the same area in violation of policy.
Violence in Juarez, across the border from the US city of El Paso in Texas, has reached critical levels as rival drug cartels battle federal authorities attempting to quell the carnage and each other for control of lucrative drug routes into the US.
More than 250 people have died in the city in the past month, prompting authorities to deploy thousands of troops to the city.
Federal authorities hope to have 7,500 troops deployed in the city by the end of this week, along with 2,000 in the rest of Chihuahua state.
The city mayor's office has also said the army will take control of the city's police force, prisons and traffic police from next week.
A two-year crackdown by Felipe Calderon, the Mexican president, on the nation's drug cartels, in which thousands of troops have been deployed across the country, has sparked brutal violence as cartels battle for turf and power, with around 6,000 people dying in the fighting last year, many of them civilians.
The US and Canadian governments have also warned tourists to stay away from dangerous border cities this spring.