Greinke sustained a broken left collarbone when Padres left-fielder Carlos Quentin charged the mound after Greinke hit him with a pitch leading off the bottom of the sixth inning.
Quentin was ejected for charging the mound. Greinke, Dodgers center-fielder Matt Kemp and Dodgers third baseman Jerry Hairston Jr. were ejected for fighting in the brawl that ensued after Quentin took Greinke down.
Greinke did not accompany the Dodgers to Arizona Friday. Instead, he consulted with a specialist in Los Angeles and the team later announced surgery would be performed and Greinke would be out about two months.
The fracas emptied both benches and erupted a second time after the Dodgers took umbrage at what they considered some inappropriate chirping about Greinke from the dugout by Padres catcher John Baker.
Tempers were still flaring after the game when Quentin and Kemp exchanged words. Kemp had been irate after a pitch sailed over his head earlier in the game, and Quentin claimed Greinke had thrown at his head.
Greinke, the 2009 American League Cy Young Award winner, denied he tried to hit Quentin, who is known to crowd the plate, but it appeared Greinke said something that caused Quentin to attack the mound.
MLB officials had not announced by midday Friday whether any disciplinary action would be taken.
Quentin "should not play a game until Greinke can pitch," Dodgers Manager Don Mattingly said.
Asked if there was bad blood between the Dodgers and the Padres, Greinke -- who joined Los Angeles this season as a free agent -- said: "Now there probably is. I don't know if there was before."