Reliever Brian Wilson exercised his $10 million player option on Friday.
Billingsley, a 30-year-old former All-Star didn't pitch last season, when he was rehabbing and needed surgery to repair a partially torn flexor tendon. He made just two starts in 2013 before needing Tommy John surgery.
Billingsley had an 81-61 record with a 3.65 ERA for the Dodgers. He won a career-high 16 games in 2008 and was an All-Star the following season. He becomes a free agent.
The Dodgers face a Monday deadline to offer Ramirez a $15.3 million, one-year qualifying offer.