Oakland manager Bob Melvin announced the plan for Griffin's surgery on Tuesday, after the pitcher got a second opinion from Dr. Thomas Mehlhoff in Houston.
Parker had Tommy John surgery on his right elbow during spring training. Parker, who had been expected to be Oakland's opening day starter, and Griffin combined for 26 victories last season.
Melvin says losing two players like that for the season is ''a difficult blow.''
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.