The clashes took place in a prison located in the province of Guayas on Wednesday evening.
"Six prisoners and five police officers were injured," SNAI said in a statement on Twitter.
Police officers remain on site to maintain order, the service said.
On Monday, clashes occurred in a prison in the Ecuadorian province of Cotopaxi. As a result of shooting between prison gangs, 15 people were killed and 20 were injured.
Riots and clashes are not uncommon in prisons in Ecuador. In early April, clashes in the prison of the town of Turi in the province of Azuay led to the death of 20 people.
In November 2021, 68 people were killed and 25 others were injured during a riot in an Ecuadorian jail in the city of Guayaquil, the same facility where more than 100 died in riots in late September.