The confrontation began at the National Penitentiary on the outskirts of the Honduran capital, Tegucigalpa.
Honduran Security Minister Armando Calidonio said police and guards were working to restore control.
"The confrontation was between two rival groups of prisoners who fired shots at each other in a territorial dispute," Mr Calidonio said.
He said officials were investigating how inmates had guns in the National Penitentiary.
Honduras' overcrowded, aging prisons have frequently been the scene of riots and fights between inmates - especially members of rival street gangs.
Nearly 600 prisoners rioted at the same facility in 2004 to protest the transfer of four of their leaders to another facility. No injuries were reported in that incident.
In 2004, a fire broke out in a cell block housing 182 gang inmates, killing more than 100 inmates.
Firefighters said the flames were sparked by overheated electrical cables from more than 75 domestic appliances the prisoners had been using.
Survivors of the fire claimed it was set deliberately by rival gang members.