Head coach Mike McCarthy took a wait-and-see approach when asked about Cobb's injury by reporters.
"It's unfortunate, but we'll see how it goes," said McCarthy, whose Packers have a 1-1-1 record.
Cobb is a huge part of Green Bay's offensive scheme, having participated in 91 percent of the Packers' offensive plays through three games. He has made 17 receptions for 194 yards and a touchdown.
However, in the last two games, he has been limited to a total of eight catches for 52 yards, but there is no indication that the hamstring injury might have been a factor.
If Cobb can't play on Sunday against the Bills, the Packers will turn to backup wide receiver Geronimo Allison, and they also have rookies Marquez Valdes-Scantling and Equanimeous St. Brown opposite No. 1 receiver Davante Adams.
Packers quarterback Aaron Rodgers has been dealing with a knee injury since the opener and also listed as questionable, but is expected to play against Buffalo.