Little suffered the injury in the first half of the Robins' 2-1 Championship defeat at Leeds on Tuesday.
The 28-year-old, who joined City from Peterborough in June 2014, has made 28 appearances for the club this season.
Leading goalscorer Tammy Abraham, 19, is still being assessed by parent club Chelsea's medical staff after suffering a thigh injury in the loss to Leeds.
Bristol City defender Mark Little will be out for four to six weeks after suffering a torn hamstring.