The wide receiver/kick returner was injured early in the fourth quarter of last Sunday's 24-23 victory against the Oakland Raiders.
Jauron said the surgery was performed on Tuesday to repair ligament damage.
The four-year veteran made a 14-yard touchdown reception after the injury.
Parrish led the NFL on punt returns in 2007 and, after the first three weeks this season, he was third overall in that category.
"We're hoping it's four to six weeks, in that range, which obviously sets us back a little bit," Jauron said following Wednesday's practice.
The former Miami (Fla.) star has made seven receptions for 60 yards with one touchdown and added 167 yards on kick returns while helping the surprising Bills to a 3-0 start and the lead in the AFC Eastern Division.
Notable deaths of 2014 [PHOTOS]