City manager Chris Hughton was counting the cost of the club's first Premier League point of the season after Bennett was ruled out.
Bennett was taken for scans after experiencing pain following Norwich's 2-2 home draw against Everton on Saturday.
The decision was made to operate on Wednesday night and Hughton expects the midfielder to be out of action for a "number of months".
Hughton told reporters in a press conference to preview Saturday's clash against Hull: "Losing Elliott is a big blow for us. It's really bad news for the player first and foremost because I felt he did well against Everton.
"He played the game on Saturday but didn't have a great reaction and we have since found that there was a knee problem that was operated on.
"It will keep him out for a number of months."
New signing Gary Hooper will also miss the trip to Hull after missing training following a shin injury suffered in the pre-season match against Panathinaikos but Robert Snodgrass has recovered from a groin injury and is likely to replace Bennett.
"Robert trained for the first time and will come into contention for the weekend," said Hughton. "Gary still hasn't trained yet. We felt progress might have been a little quicker than it has turned out."
Meanwhile, there is a good chance Johan Elmander, Norwich's new Swedish loan-signing from Galatasaray, will be involved at Hull if the club obtain international clearance in time.
The arrival of Elmander has seen Luciano Becchio linked with a move to Middlesbrough in the Championship along with centre-back Dani Ayala.
Hughton, however, refused to confirm they would be on their way before the transfer window closes next month.
"When you are a club in the Premier League there is always going to be speculation," Hughton said.
"We are making assessments of the squad. We have brought in eight players now but we have had more go the other way so we have to get the balances right. We have to feel everyone within the squad can give us that competition."
Elmander, however, was delighted with his season-long switch to Carrow Road, despite limited success in his previous Premier League stint at Bolton.
Elmander, 32, said: "I'm older and more experienced now and hopefully I can help the younger players in the team.
"When I was at Bolton Kevin Davies did that job and he was very good for everyone. At Galatasaray I was the daddy in the dressing room and hopefully I can do the same at Norwich."
Hughton added: "Yohan's very experienced and played at the highest level. Rickie van Wolfswinkel and Gary Hooper are new to the Premier League so Johan will give us something different and more experience."