The Rams have yet to clinch a playoff berth and will need a win in Week 17 or a Chicago Bears loss to secure a wild-card spot.
Los Angeles is already short-handed entering Sunday with quarterback Jared Goff out with a thumb injury. Cooper Kupp and Michael Brockers are also unavailable on the reserve/COVID-19 list, while running backs Darrell Henderson and Cam Akers are limited by injuries.
Playing without Floyd could be significant after a breakout season where he has set career highs with 9.5 sacks and 53 tackles.
The 2016 first-round pick spent the past four years with the Chicago Bears but was inconsistent after a strong rookie season. He signed a one-year deal with Los Angeles last offseason and has set himself up for a big payday in 2021.
"He has been so steady, so consistent, so versatile," Rams coach Sean McVay said Friday. "He is really affecting and influencing the game in a variety of ways."
The Rams have had the No. 1 pass defense in the NFL this season but the unit would take a major hit if Floyd is unable to play Sunday, especially against the mobile Kyler Murray.
Los Angeles is hoping to avoid missing the playoffs with a 9-7 record for the second straight year after reaching the Super Bowl in 2018.