Woods went down with what McVay called "a freak accident," and then he got up and finished practice, sources told ESPN's Adam Schefter and Dianna Russini. After conducting media interviews following practice, Woods underwent tests that confirmed the injury.
"You're sick for Robert," McVay told reporters on Saturday. "He's epitomized everything that's been right about this place. Such a great competitor. Such a tough player. Such a great football player, great person. It's so unfortunate."
McVay said Woods was running a route without a defender and put his foot in the ground weird.
"He kind of came back and said he felt OK and we ended up getting a scan, and it revealed the result that we all know," McVay said.
Beckham will make his Rams debut against the San Francisco 49ers on Monday Night Football, sources told ESPN. The 49ers have won four straight over the Rams.
"You can see he's a really sharp guy," McVay said when asked if Beckham would be ready to play Monday. "Like the look in his eye, and we'll see how he's feeling. We'll see what that looks like if we're able to utilize him, if he's able to go on Monday."
Beckham on Saturday acknowledged an increased sense of urgency due to Woods' injury.
"Whatever I can do to help," Beckham said. "I'm trying to learn the playbook as fast as possible, and if there's something [McVay] needs me to do, I'm always willing to do whatever it is. I guess we'll see come Monday."
The loss of Woods, however, cannot be overstated as the Rams aggressively pursue a trip to Super Bowl LVI at SoFi Stadium in February.
Since the Rams signed Woods in 2017, the ninth-year pro has played a critical role in the passing game as a receiver, blocker and even out of the backfield.
This season, Woods is second on the team behind Cooper Kupp, the NFL's leading receiver, with 45 catches for 556 yards and four touchdowns. Woods also has rushed for 46 yards and a touchdown on eight carries. His 70 targets this season were tied for 15th in the NFL entering Week 10.
"You don't ever replace a player like Robert Woods, but you do have to adjust and adapt accordingly," McVay said, "because him, Cooper ... What these guys have been able to do is very unique in all the different ways they contribute to the offense, not exclusive to when they touch the ball."
The Rams' offense under quarterback Matthew Stafford ranks No. 3 in the NFL, scoring an average of 29 points per game. Stafford has passed for 23 touchdowns this season, which ranks second only to Tom Brady's 25.
Second-year pro Van Jefferson, who has spent more than a year learning from Woods, is tied for third on the team (alongside tight end Tyler Higbee) with 46 targets and will be tasked with a larger role.
Woods' injury once again leaves the Rams thin at the receiver position after rookies Tutu Atwell and Jacob Harris suffered season-ending injuries. Earlier this week, a waiver claim to bring back released wideout Josh Reynolds fell short as he was picked up by the Detroit Lions.
Rookie seventh-round pick Ben Skowronek and undrafted free agent J.J. Koski, who was signed from the practice squad earlier this month, will be counted on for depth behind Kupp, Jefferson and Beckham. Skowronek and Koski have combined for three catches for 30 yards.
Since the Buffalo Bills selected Woods with a second-round pick in 2013, he has never missed more than three games in a season.
At the outset of last season, Woods agreed to a four-year, $65 million contract extension that begins in 2022.
In 4½ seasons with the Rams, Woods has 367 catches for 4,626 yards and 23 touchdowns and has rushed for 485 yards and five scores.
ESPN's Nick Wagoner and The Associated Press contributed to this report.