Doolittle had been on the 15-day DL with a strained left shoulder, but the left-hander is not close to returning. Moving him to the 60-day DL opened up a roster spot for Griffin, who is recovering from 2014 Tommy John surgery.
Griffin isn't going to be activated to the 25-man roster in the immediate future either, manager Bob Melvin said before Saturday's game against the Angels. He'll continue to pitch with Nashville, where he has been rehabbing -- he pitched a rehab start Friday night.
"He's not ready to be here right now, with it being his first outing of five innings and 80 pitches," Melvin said.