"I don't think it's good," Rams coach Sean McVay told reporters after the game. "We'll get the MRI, but it doesn't look good right now."
Kupp, 25, recorded 40 receptions for 566 yards and six touchdowns in 2018. He missed two games earlier in the season with a knee injury and has been one of Jared Goff's favorite targets when on the field.
The Rams will likely place more of a responsibility on Brandin Cooks and Robert Woods in Kupp's absence. Josh Reynolds caught a pair of touchdowns with Kupp out of the lineup initially and may see an increased role the remainder of the season.
KhaDarel Hodge is listed behind Kupp on the Rams depth chart and caught one pass for 14 yards against Seattle.
Kupp in all likelihood will be able to return for the beginning of the 2019 season.