McCourty, who did not return to the field after halftime, underwent some follow-up tests Monday.
Coach Bill Belichick gave his standard injured-player response Monday regarding McCourty.
"We'll see on Wednesday," Belichick said, referring to the day the Patriots return to practice.
McCourty, whose six interceptions rank him among the league leaders, is a legitimate contender for the Defensive Rookie of the Year award. If McCourty can't play Sunday against the Green Bay Packers, Darius Butler, who has had an uneven season, likely would replace him.
Butler, a second-round pick in 2009, was benched after the second game of the season when the New York Jets' Braylon Edwards beat him for a touchdown and a two-point conversion. Butler's playing time dwindled to the point where he was inactive for one game, but he has been playing more lately. He played the second half Sunday in place of McCourty.
"Darius has played a lot of football for us over the last couple of years," said Belichick. "If we didn't have confidence in him, we wouldn't put him out there."
Butler, who starred at the University of Connecticut, said Monday he was up to the challenge.
"It's business as usual for me," said Butler. "I just work to prepare myself to be a starter. I'll be ready when my number is called."