Greinke was hurt Thursday night in a bench-clearing brawl with the Padres that started when San Diego slugger Carlos Quentin charged the mound after he was hit on the arm by a pitch.
The Dodgers said Greinke was examined Friday by Dr. Neal ElAttrache in Los Angeles and had a CT scan. ElAttrache and Dr. John Itamura will operate Saturday at White Memorial Hospital in Los Angeles to place a rod in the clavicle to stabilize and align the fracture.
According to a source close to the situation, the hope is that by implanting the rod, Greinke will be able to throw as soon as pain permits, perhaps as early as a week to 10 days post-surgery.
Speaking to reporters before his team played Arizona on Friday night, Dodgers manager Don Mattingly said he wasn't surprised by the extent of Greinke's injury.
"We knew last night, for the most part, that it was going to be extended," he said. "It's unfortunate."
Greinke, the 2009 AL Cy Young Award winner, signed a $147 million, six-year contract with the Dodgers during the offseason.
"Obviously, the attention that he got this winter and things that he's done in his past tell you he's hard to replace," Mattingly said. "I guess we're in a sense fortunate that we have a few extra starters this spring, and right now it's a good thing."
Lilly has been on the 15-day disabled list since March 28 and was slated to throw a bullpen session Friday. Capuano, now in the Dodgers' bullpen, is a former starter.
Los Angeles placed Greinke on the 15-day disabled list and recalled right-handed reliever Shawn Tolleson from the minors to take the roster spot.
Mattingly, far calmer than he was in the heated aftermath of the fight, said he will wait to see the outcome of Lilly's bullpen session before making a decision on a replacement for Greinke.
"We still have a few days to make a decision," he said. "We don't have to announce a starter. For another day, I can avoid you."
Quentin was suspended eight games and Dodgers infielder Jerry Hairston Jr. one game by Major League Baseball on Friday night for their roles in the brawl.
After the teams had started heading back to their benches and bullpens, Hairston went running across the field yelling and pointing at someone in the Padres' dugout and had to be restrained. That led to more pushing and shoving, and nearly a second melee.
Hairston claimed a Padres player -- whom he wouldn't name -- was making fun of the fact that Greinke had been injured.
Quentin and Hairston both played Friday night, pending appeal by the players' association. Both players were fined as well.
No discipline was announced for Greinke or Dodgers outfielder Matt Kemp, both ejected along with Quentin and Hairston.
Information from ESPN's Stephania Bell and The Associated Press contributed to this report.