Greinke -- a 2009 American League Cy Young winner -- is expected to miss eight weeks, the team said late Saturday.
Greinke was injured Thursday in a game against San Diego 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 and has been suspended for eight games by Major League Baseball. 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.
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 denied he tried to hit Quentin, who is known to crowd the plate, but it appeared the hurler said something that caused Quentin to charge the mound.
Greinke is 1-0 with an ERA of 1.59, 10 strikeouts and one walk in two starts this season. He has held opposing batters to an overall .175 batting average.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Wisconsin business offering 'therapeutic cuddling' forced to close