Officials initially put the death toll at five, but later said mutilated bodies were found strewn throughout the wing where shots were heard early Thursday.
According to Roberto Alvarez Heredia, security spokesman for the state of Guerrero, the fight started in the prison's maximum security wing.
State police have temporarily taken control of the prison, backed by federal police and the army, which set up a security cordon outside. Three more inmates were wounded in the violence, Mr Alvarez said.
A report issued last month by Mexico's governmental rights agency said numerous country's prisons are unsafe, overcrowded and understaffed. The facility can house 1,624 inmates, yet there are 110 women and 1,951 men incarcerated.
It was the latest deadly riot in Mexico's chronically overcrowded prisons, where corruption abounds, inmates often have de facto control, and contraband weapons and drugs are rife.
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Early previous year, 49 people died in a battle between members of the feared Zetas drug cartel and rivals at a prison in the northern industrial city of Monterrey.
Acapulco, one of Mexico's most famous beach resorts, was once a playground for Hollywood stars but in recent years has been roiled by vicious gang warfare.
In March 2017, 29 accused drug cartel members allegedly tunneled their way out of a prison in Tamaulipas state.
The prison carnage fell on the same day U.S. Department of Homeland Security Secretary John Kelly was visiting Guerrero, in Mexico's southwest.
Kelly, is one of the main links between the Mexican government and the Trump administration on migration and security cooperation.
Guerrero has been one of Mexico's most violent states and the once-glamorous resort of Acapulco has struggled with a high number of killings.