"We were hoping that wasn't going to be the case," Oakland manager Bob Melvin said before Tuesday's game in Texas.
"Losing two guys like that for the entire season is a difficult blow. One's a blow, two is tough. You move on, but you certainly have a lot of sympathy for the two guys that are having to go through that, because they've meant so much to this team over the last couple of years."
Parker, who had been expected to be Oakland's opening day starter, had Tommy John surgery on his right elbow during spring training.
Griffin will have the surgery after getting a second opinion Tuesday from Dr. Thomas Mehlhoff in Houston.
Melvin said he didn't know the specifics of the surgery Griffin will have or how extensive it would be. He had spoken only briefly to Griffin.
"He's always pretty happy-go-lucky, in good spirits," Melvin said. "I think the fact that he's having it done this early gives him a light at the end of the tunnel to pitch next season. The longer that goes on, the more difficult it is to come back and get semi-close to a full season. He's looking at it very positively."
Parker and Griffin combined for 26 victories last season.
Griffin was 14-10 with a 3.83 ERA last season after making his major league debut in 2012 going 7-1 with a 3.06 ERA in 15 starts for the A's. Parker went 13-8 in 2012, and was 12-8 last season.