Fletcher was covering Sims-Walker on a pass play and landed awkwardly on his right knee. Sims-Walker hurt his shoulder on the play.
Coach Steve Spagnuolo says the extent of the injuries wasn't known. Fletcher says he will get an MRI but the injury isn't a bad one.
Defensive coordinator Ken Flajole pulled a groin demonstrating a play as a linebacker. He said: "I was trying to be a young guy and help on the pass drill and I realized I'm an old guy."
The Rams (0-4) won't play again until an Oct. 16 game at Green Bay.