The injury occurred during the third quarter of Sunday's 30-23 loss to the Green Bay Packers when Davis got his leg stuck in a pile of players. It's another huge blow to Carolina's defense, which lost Jon Beason for the year with a torn Achilles in the season opener against the Arizona Cardinals.
"He trained so hard to come back," Rivera said of Davis. "Everything was coming together, and he was playing really well. It was just like Jon last week, where he was looking good and playing well and them something like this happens. We'll go forward and see how things unfold."
Davis wrote on Twitter: "I would like 2 take the time and thank every1 that has supported me over my career."
The Panthers signed Davis to a five-year, $35.5 million contract extension in July, but just $8 million of that money was guaranteed -- a $7 million signing bonus and $1 million base salary in 2010. The move allowed Carolina to avoid a huge long-term salary cap hit in case something like this happened once again.
Omar Gaither replaced Davis on Sunday, but Rivera wouldn't say who'll start this weekend against the Jacksonville Jaguars. Along with Gaither, the Panthers have other options, including Jason Williams, Thomas Williams and Jordan Senn.
Davis first tore his right ACL on Nov. 8, 2009 against the New Orleans Saints and again during June 2010 minicamps.
The Associated Press contributed to this report.