Kazee suffered the injury in the second quarter of Monday night's loss to the Green Bay Packers and was carted off the field. He fell to the ground, grabbing the back of his left leg, and was in obvious pain while being checked by the training staff.
Quinn and team owner Arthur Blank consoled Kazee, who is in the last year of his contract, after the game. The coach told reporters that Kazee, who was replaced by Sharrod Neasman, had a "serious injury."
The Falcons entered the game already down two safeties with Keanu Neal sidelined by a hamstring injury and Ricardo Allen out with a hyperextended elbow. The Falcons started Kazee and rookie Jaylinn Hawkins at the safety spots. Hawkins also left the game with a concussion, and Jamal Carter played the second half in his place.
Atlanta also entered the night missing starting cornerback A.J. Terrell, who remains on the reserve/COVID-19 list, and veteran corner Darqueze Dennard, who is on injured reserve with a hamstring injury.
Kazee, a fifth-round draft pick out of San Diego State in 2017, tied Kyle Fuller and Xavien Howard for the league lead with seven interceptions in 2018. He has 10 interceptions and three forced fumbles in 52 career games.
The Falcons experimented with playing Kazee at nickelback but eventually put him back in his comfortable zone at free safety based on his ability to make plays on the ball.
Allen, who is working his way back from the hyperextended elbow, could reassume a starting role at free safety once healthy with Kazee out for the season.
ESPN's Vaughn McClure contributed to this report.