The hard-throwing right-hander had already been scratched from his scheduled start Friday with arm fatigue. Long reliever Cory Rasmus is scheduled to take Richards' place in the opener of the Angels' series against Tampa Bay.
The 27-year-old Richards made his first Opening Day start for the Angels last month, cementing his rise to the top of the staff, which began in his breakthrough 2014 season. He is 1-3 with a 2.34 ERA in six starts this season, repeatedly facing other teams' aces and getting meager run support from his light-hitting teammates.
Richards went 13-4 with a 2.61 ERA in 2014 while often pitching spectacularly for the Angels, who finished with 98 wins and the majors' best regular-season record. But Richards needed season-ending knee surgery that August after getting hurt while covering first base, and Los Angeles didn't win a playoff game.
Richards then went 15-12 with a 3.65 ERA last season, emerging as a dependable No. 1 starter. He signed a one-year, $6.425 million deal for the current season to avoid arbitration, and he won't be eligible for free agency until the 2018 season.
The injury would be the biggest blow yet to the Angels' suddenly beleaguered rotation, which had been one of the few areas with depth for a franchise whose farm system is poorly regarded.
Wilson, who is making $20 million this season, has shoulder tendinitis that has kept the left-hander off the mound for nearly two months. The Angels don't know when he will return.
Skaggs had been pitching in the minors until he was shut down last week to recover from biceps tendinitis.
The Angels are likely to be forced to recall right-hander Matt Shoemaker, who was sent to the minors last weekend after performing poorly in their rotation in April.
Information from The Associated Press was used in this report.