Childs, a junior, has 46 catches for 659 yards and six touchdowns this season, topping 80 yards receiving in four games this year for the Razorbacks (No. 18 BCS, No. 17 AP). He will undergo surgery later this week.
"It's a big loss for us," Petrino said. "He's a great football player, tremendous competitor. It's something that we'll have to replace with a number of people. You're not going to replace Greg Childs with just one guy."
In his career, Childs has 1,829 yards and five touchdowns.
Childs injured his knee while making a 17-yard catch early in the fourth quarter of a 49-14 win over the Commodores. The reception broke the school record for yards passing in a game for quarterback Ryan Mallett, who finished with 409 yards passing in the win.
"It's just something special about Greg when he gets the ball in his hands," Mallett said. "Everybody expects him to go score."
Childs injured an ankle a week earlier against Mississippi but returned to practice last week and was cleared to play against Vanderbilt. He finished the game with five catches for 87 yards before leaving after making the catch from Mallett and spinning to try and reach the end zone.
"That's definitely tough for us because Greg is an awesome player," Arkansas defensive end Damario Ambrose said. "He's very dynamic, fast and can jump out the gym. It's tough to be losing him, but we have tons of other receivers on our team that can step up."
Childs was one of three Arkansas receivers to miss time against Vanderbilt. Joe Adams, the team's second-leading receiver, missed the entire game with an ankle injury he suffered against Ole Miss. Also, the team's third-leading receiver, Jarius Wright, missed action briefly in the second half after being on the receiving end of a big hit and suffering from dehydration.
The injuries didn't slow the Razorbacks, who gained 555 yards in the win and are second nationally in passing offense at 360.2 yards per game. Sophomore Chris Gragg and freshman Julian Horton combined for four catches for 113 yards for Arkansas in place of the starters, and eight Razorbacks caught passes from Mallett.
"We do feel like we have good depth and we have different guys we can get the ball to," Petrino said. "They'll look forward to the opportunities."
Petrino said Adams made "significant improvement" from his ankle injury over the weekend, and he was hopeful the junior would be able to practice this week.
Joe Schad is a national college football reporter for ESPN. Information from The Associated Press was used in this report.