Burrow left the game with 8:36 left in the second quarter and had to be helped off the field, unable to put any weight on his foot.
The three-month stint means that Burrow will likely need surgery.
Burrow was later seen with a boot and crutches following the game.
Cinci's franchise quarterback was trying to escape the pocket, but Jaguars defensive end Arik Armstead wrapped Burrow up by the foot, causing the injury.
Burrow completed 7-of-13 passes for 76 yards and one touchdown before his injury.
He tossed the Bengals' first touchdown of the game to wide receiver Ja'Marr Chase right before the first quarter ended.
Cinci would later go on to win the game 31-27 as they improved to 2-0 on the season.
Backup quarterback Jake Browning came in for Cinci, completing 21-of-32 passes with 241 yards, two touchdowns, and three interceptions. Browning would also leap for a QB sneak touchdown to win Cincinnati the game at the end of the fourth quarter.