Davis made two receptions for 9 yards against the Cincinnati Bengals, the first one for a 5-yard score in the second quarter. The injury reportedly occurred on his second reception, when Davis got up limping.
He was carted to the locker room after trainers looked at the knee.
NFL Network was first to report the news of Davis' injury.
Even without an official diagnosis after the game, Packers coach Matt LaFleur suggested Davis would miss significant time.
"My heart hurts for him," LaFleur said. "We're going to miss him."
Davis, 26, was a sixth-round pick by the Jacksonville Jaguars in the 2020 NFL draft. He played eight games for the Jaguars in 2020, then signed with the Packers in 2021.
In 31 games (one start) in Green Bay, he has caught eight passes for 61 yards. While he has played just 17% of the team's offensive snaps, he's been a key contributor on special teams, taking part in 81% of snaps.
Information from Reuters was used in this report.