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. "So it's gonna take him some time to get to where we're looking to potentially bring him up here."
Griffin allowed four home runs in 4 1/3 innings, but Melvin said he was told Griffin commanded and mixed his pitches well.
"I know he felt good, and that's what we're looking for right now, to move him along," Melvin said. "His velocity probably isn't where we would see it normally -- he's probably still [around] 86. But he's trying to throw strikes, he's trying to get ahead. He's trying to stay out there as long as he can to get his pitch count up, too."
Melvin also noted that Griffin didn't walk any batters and that it was his longest time on the mound during his rehab so far.
• First baseman Ike Davis (strained left quad) also made a rehab start for Nashville on Friday, going 1-for-3 with some hard-hit balls. Melvin said Davis would play seven innings for Nashville on Saturday night.
• The A's signed outfielder Dayan Viciedo, who was released by the Blue Jays in the offseason, to a Minor League deal Friday.
"We had talked about him in the spring," Melvin said. "Any time you can increase the depth with a guy with a track record of a power bat in the big leagues, it's nice to be able to have him in our organization."
• The A's agreed to terms with nine more selections from the Draft on Saturday, including third-round pick Dakota Chalmers, a right-handed pitcher from North Forsyth (Ga.) High School. MLB.com's Jim Callis reported the Chalmers deal at $1.2 million.
Oakland has now signed or agreed to terms with 27 of its 40 picks.
The other players to agree to terms Saturday were first baseman Chris Iriart (12th round, Houston), second baseman Ryan Howell (15th, Nevada), right-hander Dustin Hurlbutt (16th, Tabor), catcher Brett Sunde (18th, Western Michigan), outfielder Seth Brown (19th, Lewis-Clark State), left-hander Andrew Tomasovich (21st, Charleston Southern), catcher Jordan Devencenzi (26th, Nevada) and shortstop Tim Proudfoot (35th, Texas Tech).