Greinke was expected to be out for eight weeks, the Dodgers said Friday afternoon. He was scheduled for surgery on Saturday.
Padres slugger Carlos Quentin was suspended eight games and Los Angeles infielder Jerry Hairston Jr. suspended one game by Major League Baseball for their roles in the brawl.
It all started when Greinke hit San Diego's Carlos Quentin on the left shoulder with a pitch.
The slugger started walking toward the mound and Greinke appeared to say something. Quentin then charged Greinke. They dropped their shoulders and collided, and Quentin tackled the pitcher to the grass. Players from both sides ran onto the field and jumped in.
After the teams started going back to the dugouts and bullpens, Jerry Hairston Jr. came running across the field yelling and pointing at someone in the San Diego dugout. He had to be restrained.
Quentin and Hairston are playing, 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.
The Dodgers ended up winning the game 3-2, but the fighting continued off the field. No punches appeared to be thrown, but Matt Kemp confronted Quentin nose-to-nose as the two were leaving Petco Park. Padres pitcher Clayton Richard stepped between them, and security broke it up.
Greinke twice hit Quentin with pitches when they were in the American League. Quentin said his history with Greinke has been "well-documented. That situation could have been avoided. You'd have to ask Zack about that."
"I've been hit by many pitches," said Quentin, plunked more often than any other major league hitter since the start of 2008. "Some have been intentional, some have not been. For the amount I have been hit and my hitting style, I'm going to repeat: I have never reacted that way."
Greinke, on the other hand, said the hit was not intentional.
"I never hit him on purpose," said Greinke. "I never thought about hitting him on purpose. He always seems to think that I'm hitting him on purpose, but that's not the case. That's all I can really say about it."
Some baseball fans said that's just how the game goes.
"It's fun to watch, and obviously, it got a little bit out of hand. But other than that, it's all part of the game," said baseball fan Eli Martinez.
Quentin, Kemp, Hairston and Greinke were ejected from Thursday's game. The two teams meet again Monday night when the Padres head to Los Angeles for a three-game series.
The Associated Press contributed to this report.