Billingsley bruised the index finger on his right hand during a bunting drill on March 15. He was scratched from a start earlier in the week.
Manager Don Mattingly says Billingsley might start the second game on April 2 against San Francisco.
Billingsley says he wants to work on his curveball, which means putting more pressure on the tip of his injured finger. He plans to throw curves in a bullpen session Monday.
Billingsley struck out seven against Cleveland minor leaguers. He didn't throw any curves, but expects to be OK to start the season.
"As long as there are no setbacks, I plan to be there," he said.