The A's officially placed opening-day starter Brandon McCarthy on the 15-day disabled list with a recurring shoulder strain retroactive to Wednesday. Oakland also called up reliever Evan Scribner and optioned infielder Eric Sogard to Triple-A Sacramento.
To clear a spot on the 40-man roster for Griffin, the A's designated Danny Farquhar for assignment.
Griffin has a combined 6-3 record and a 2.66 ERA in 15 games with Double-A Midland and Triple-A Sacramento this season. The 24-year-old was drafted by the A's in the 13th round of the 2010 draft.