The unrest took place on Sunday east of the capital in El Porvenir penitentiary, according to Heraldo.
At least two people were reportedly transferred to a hospital with stab wounds. There have been no reports regarding the emergency measures taken by the prison authorities.
On 21 December, 18 people were killed and 16 others were injured in fighting between prisoners in Honduras' northern port town of Tela.
The government of Honduras declared a state of emergency in the country's prison system on 18 December and transferred control of the penitentiary institutions and prisons to the armed forces and police.
According to reports, there are currently about 20,000 inmates in Honduran prisons despite the capacity to only house 8,000.