Police were notified of the incident at 8:30 p.m. and arrived to find that several of the others involved in the confrontation had left the scene.
Police arrested the man with the machete and recovered the weapon. The rugby match continued without any further incident, police said.
The man, identified as an 18-year-old Santa Rosa resident, was booked into Sonoma County Jail on suspicion of possession of a deadly weapon.
Those involved with the incident are also believed to be involved with gangs and the suspect was also booked for a gang enhancement.
Police also found a 14-year-old male with one of the two groups who had been reported as a missing person. He was returned to his parents.