Wilson, who was one of the Angels' big free-agent signings this winter, has given up 10 runs in 9 2/3 innings since dominating the Blue Jays on May 5. In his start Thursday against the White Sox, Wilson walked six batters in 3 2/3 innings.
The Angels team doctors believe Wilson had a stomach virus Thursday, which may have contributed to his poor performance.
"I just couldn't really get anything going," Wilson said. "I couldn't find the strike zone. I tried to make adjustments and it didn't work. I just sucked today."
While Wilson has had a disappointing May by his standards, Godfrey hasn't pitched in the Major Leagues since April 20. He made three starts at the beginning of the season before being sent back to Triple-A Sacramento. Now, with right-hander Brandon McCarthy on the disabled list with a strained right shoulder, Godfrey will get another chance.
Godfrey made five starts in Sacramento, going 3-0 with a 1.21 ERA.
A's: Cook continues scoreless run
Right-hander Ryan Cook pitched another scoreless inning Monday and has not allowed a run in 21 2/3 innings this season. He has appeared in 19 games and become one of the A's most trusted relievers.
Cook's streak to start the season is the longest in A's history for a player on the Opening Day roster dating back to 1918.
The A's 2-1 victory Monday night was just their eighth one-run game, the second fewest in the Major Leagues. The win improved their record in those games to 6-2.
Angels: Bullpen continues hot streak
Relievers Hisanori Takahashi and Jason Isringhausen combined for 1 2/3 scoreless innings Monday night, extending a stretch where the Angels bullpen has given up just three runs in 22 1/3 innings.
After calling up right-hander Bobby Cassevah on Monday, the Angels have eight relievers on their 25-man roster giving manager Mike Scioscia even more options should his starters falter.
The Angels have struggled hitting with runners in scoring position in the past five games, going 5-for-48. In that stretch, they have scored 13 runs and are 1-4.
The A's are 8-5 against left-handed starters. That includes a 4-2 victory against Wilson and the Angels on April 19 in Los Angeles.
Since scoring six runs in the teams' first meeting this season, the Angels have scored just 10 runs in their last six games against the A's.