The injury had been reported earlier by The Boston Globe.
Patriots coach Bill Belichick confirmed Monday afternoon that Wilfork's season is likely over.
"It doesn't look too good for Vince," Belichick said during his weekly interview on Boston sports radio station WEEI. "I think he's got a pretty serious injury, and it's probably unlikely that he'll be able to play again this year."
Earlier in the day, Belichick said only that Wilfork was undergoing tests and that he didn't know much more than that. A few hours later, he went public with the news.
"Very disappointed for Vince," Belichick said. "He's worked hard to prepare for the season. He's a true professional, gives us great leadership on and off the field. Great example for the younger players as well as the veteran players. He has a real commitment to the team and to winning."
Wilfork left the Patriots' 30-23 win against the Atlanta Falcons in the first quarter, limping off the field on the Falcons' first possession. He did not return.
He was later taken to the locker room on the back of a cart.
"We'll just have to see how things come together for him," Belichick had said earlier. "Obviously if he's not there, everybody will have to pull a little bit more weight on their end."
Belichick was seen speaking with Wilfork's wife, Bianca, outside the team's locker room after the game.
Wilfork, one of the team's captains, is a perennial Pro Bowler and vital cog to the team's defense, particularly against the run.
"Clearly, there are no Vince Wilforks just standing around out there on the corner waiting to sign with the Patriots or some other NFL team," Belichick said on WEEI. "He is a special player, one of the very best at his position. There's no way that you would replace him with one guy -- that's totally unrealistic. But we'll try to do what we can to make our team as competitive as possible with the 46 guys we put out there against Cincinnati this Sunday."
According to ESPN Stats & Information, the Patriots allowed 4.1 yards per rush with Wilfork on the field over the past five seasons, which is ninth-best in the NFL. When Wilfork was off the field, the Patriots ranked last in yards per rush allowed (5.0).
"Well, to say we'll miss him is an understatement," Patriots quarterback Tom Brady said Monday in a radio interview with Jim Gray. "His presence in the locker room and on the field is really unmatched, so it will be a team effort.
"I know Coach Belichick said there's no Vince Wilforks on the street corner waiting to sign with the Patriots, which is the truth, but we're going to have to find a way to -- in a group effort -- replace such a valuable player."
The Patriots have been thin at defensive tackle since training camp started in late July, in part because Armond Armstead opened on the non-football injury list after undergoing surgery for an infection. Armstead remains on the non-football injury list, leaving the Patriots with Wilfork, fellow veteran Tommy Kelly and rookies Joe Vellano (undrafted) and Chris Jones (sixth-round pick from the Houston Texans claimed on waivers) at defensive tackle.
"Obviously Vince is a huge asset to our team not only on the field, but off the field," fellow defensive captain Jerod Mayo said. "And he's a great leader, he demands double-teams in the run game, and he also coordinates some of the rushes in the passing game as well."
Information from ESPNBoston.com contributor Field Yates was used in this report.