Kupp appeared to pull up during a route, according to head coach Sean McVay, who did not provide specifics on the injury and had not been briefed by the team medical staff at the time of his news conference.
"I hope he's OK," McVay said, via The Athletic's Jourdan Rodrigue.
The team specified that it was a hamstring injury later Tuesday evening.
The All-Pro wide receiver has terrific chemistry with quarterback Matthew Stafford and is an invaluable piece to the Rams' chances of returning to a championship level after L.A. limped to a 5-12 record during its 2022 Super Bowl defense.
Kupp was one of many high-profile Rams players to fall prey to injury last year. He suffered a high ankle sprain during a Week 9 contest, underwent surgery and did not suit up again.
Despite missing the final eight games, Kupp led the team across the board with 75 catches, 812 yards and six receiving touchdowns.
All eyes will be peeled on any updates in the near future.