Thompson will be out indefinitely, according to Panthers coach Frank Reich, who described the injury as "significant." Thompson will undergo further evaluation Tuesday.
The Panthers initially announced Thompson was doubtful to return with a shin injury, then said after halftime that he was out for the rest of the game with an ankle injury.
Thompson, a senior member of the Carolina defense, was injured when Saints left tackle Trevor Penning was slung to the ground by defensive end DeShawn Williams. The full force of the 325-pound Penning landed on the back of Thompson's leg and ankle.
Carolina players kneeled while team physicians attended to Thompson, and gathered around him when he was loaded onto the cart. Thompson raised his right hand and index finger as he disappeared into the Bank of America Stadium tunnel.
Thompson led the team in tackles last season with 135. He was making the transition from outside linebacker to inside as Carolina transitioned from a 4-3 to a 3-4 scheme.
Fellow inside linebacker Frankie Luvu talked to Thompson at halftime and told him he had his back.
"He's a big part of our defense," Luvu said. "It goes above and beyond what he does for this defense and this team."
It was the second straight week the Panthers lost a key member of the defense for an extended period. Cornerback Jaycee Horn suffered a severe hamstring injury in the opener that required a procedure that forced the Panthers to place him on injured reserve.
He will miss at least the next four games and likely will be out longer.
Thompson was replaced in the lineup by Kamu Grugier-Hill, who had six tackles and a sack.
"Shaq's the best linebacker I've played with on any team," Grugier-Hill said. "What he means to this team, what he means to this city, it's heartbreaking.''