The injury appeared to happen on a noncontact move in which Olsen misstepped.
After the game, Olsen said that he ruptured the "plantar" on his right foot and that his season was over.
"It's kind of one of those things where it was a matter of time," Olsen said. "We kind of pushed this foot I think as far as possible the last two seasons, and today it just kind of had enough."
Olsen said his foot has been bothering him the past few weeks, but he has managed the pain.
"I've been sore," he said. "It was feeling all right today. On that play, I just went to push off and it ruptured my plantar [fascia]. Like the bottom tissue in my foot.
"It all stems from what I've got going on and the amount of trauma it's had the last two seasons. We got as much out of it as we could have. Finally, my foot just had enough."
Olsen said he knew "right away" what happened on the first play of the second quarter when he came out of his stance.
"It kind of popped on me," he said.
Earlier, coach Ron Rivera said "we'll see" when asked whether Olsen was out for the year.
It is the same foot that forced Olsen to miss three games earlier this season and the same one that required surgery last year and kept the 33-year-old out nine games.
Olsen didn't want to consider this might be a career-threatening injury.
"I've got to get this foot put back together a little bit," he said. "It's been a long time since my foot has been normal."
Olsen did not have surgery after reinjuring the foot in the opener against Dallas because the pins from last year's surgery kept the bones from completely breaking.
From 2014 to '16, Olsen became the first tight end in NFL history to have three consecutive seasons of at least 1,000 yards. His production this season has dropped significantly with Carolina going more to young, dynamic receivers such as DJ Moore, Curtis Samuel and running back Christian McCaffrey.
Olsen has 27 catches for 291 yards and four touchdowns this season.
"It's just tough, to go 10 years and not really have anything and then have one little injury stall me for the good part of two seasons is frustrating," Olsen said.