The source said the Rams will be cautious with Kupp's injury but that he could be back "for scrimmages in a few weeks."
Kupp, the MVP of Super Bowl LVI, walked off the field with the training staff about 30 minutes into a two-hour workout at UC Irvine. Matthew Stafford and other players didn't see exactly what happened, but coach Sean McVay said he was told Kupp "came up a little bit in a red zone route."
A team spokesperson confirmed the injury to reporters later Tuesday.
"Obviously, we're much better when he's here, and we hope he's going to be OK," McVay said. "If he's not, we'll see what happens, but the practice had to go on."
Kupp is returning for his seventh NFL season after missing the final eight games of 2022 with a high ankle sprain. He also missed the final eight games of his second NFL season in 2018 with a torn knee ligament.
Kupp won the NFL's triple crown of receiving in 2021, leading the league in catches (145), receiving yards (1,947) and touchdowns (16). He starred during the Rams' playoff run, culminating in two touchdown catches in the Super Bowl, including the winner with 1:25 to play.
He had 75 catches for 812 yards and six touchdowns in nine games last season before his ankle sprain.
Kupp is one of just a few key players left with the Rams, who are likely to field the NFL's least experienced roster this season after parting ways with most of their veteran depth in the offseason. Stafford and Aaron Donald are also back with the Rams, who went 5-12 last year in the worst season in league history for a defending Super Bowl champion.
The 30-year-old Kupp is expected to be Stafford's go-to target again this fall.
"I just want to know what's going on," Stafford said. "That's the main thing, and I'll figure that out at some point. But I trust our guys, and whatever is going on, I know he'll do everything he can to work through whatever is going on and be back out here whenever it's the right time."
The Rams open the preseason against the Los Angeles Chargers on Aug. 12.
The Associated Press contributed to this report.