A 12-year-old boy, who was watching the event, on Sunday evening in the town of Cuajinicuilapa, is among the victims.
Another seven people were injured.
There are conflicting accounts of the incident - with some reports saying that it was caused by a row between rival groups at the fight, others that gunmen stormed the venue.
Officials told the AFP news agency that the shootout broke out after an argument between two groups who were watching the event.
But local media said that the victims were killed by unidentified gunmen, who stormed the arena just after 21:00 local time (03:30 GMT) and began shooting randomly.
Mexico's powerful criminal gangs are active in Guerrero, one of the country's most troubled states. Last year's disappearance of 43 students in the town of Iguala exposed the depth of the problem.
At least 10 people have been killed in a shootout at a cockfighting event in the restive central Mexican state of Guerrero.