Quentin rushed the mound after he was hit in the upper left arm by a pitch from Zack Greinke. The two players lowered their shoulders and Quentin slammed into Greinke, who broke his left collarbone in the wild fight that ensued.
Hairston nearly incited a second melee when he ran across the field yelling and gesturing at someone in the Padres' dugout.
Quentin and Hairston both played Friday night, pending appeal by the players' association.
Quentin also was fined $3,000. Hairston was fined, too, but the amount wasn't immediately known.
No discipline was announced for Greinke or Matt Kemp, both ejected along with Quentin and Hairston.
Quentin was gone by the time the clubhouse was opened to reporters following San Diego's 7-5 loss Friday night to the Colorado Rockies, which dropped the Padres to 2-8.
"We expected the worst and hoped for the best," manager Bud Black said. "We know it varies from case to case. I think eight was on the high side."
MLB is believed to be investigating Kemp's confrontation with Quentin as the players were leaving Petco Park after the game. The two went nose-to-nose before Padres pitcher Clayton Richard got between them. Police and security moved in and broke it up.
Greinke is scheduled to have surgery Saturday and is expected to miss eight weeks.