Billingsley's start to 2013 was delayed amid a recovery for a bruised index finger he suffered during bunting drills in March.
He was limited to 25 starts in 2012 after he experiencing elbow tightness in August. He was placed on the 60-day disabled list two weeks later, ending his season.
Billingsley, 28, is 81-61 with a 3.65 ERA in eight major league seasons, all with the Dodgers.
The Dodgers have gone from a surplus of starting pitching to a deficit in a span of 10 days.
First Zack Greinke broke his collarbone in a confrontation at the mound with San Diego's Carlos Quentin. Then Chris Capuano went on the disabled list with a hamstring injury before Billingsley was forced to the DL.
The Dodgers previously had traded starter Aaron Harang to Colorado on April 6 when it became apparent there wasn't a spot for him in the rotation.
Manager Don Mattingly said the Dodgers expect to learn more about the severity of Billingsley's injury after he has an MRI on his elbow.
In the meantime, the Dodgers are trying to regain their equlibrium under trying circumstances. They brought a six-game losing streak into Sunday's matinee in Baltimore.
"We're going through a little bit of a rough time,'' Mattingly said. "Obviously, as a team, it's been a little bit of a battle to try to get a win on the board. It seems to be a little bit of piling on. But that's just the way it is. Nobody is going to sit there and feel sorry for us. We have to go out and play and win a game.''
Information from ESPN.com senior writer Jerry Crasnick was used in this report.