A source told NFL.com that the injury is "feared to be serious."
Graham pulled in just one catch for 13 yards before leaving the game on Thursday at CenturyLink Field in Seattle. He had 34 catches for 452 yards and two scores on the season, before departing from the game against his former team.
Graham missed practice leading up to the game due to a knee injury, before being removed from the injury report.
Packers coach Mike McCarthy told reporters that he didn't know exactly when Graham suffered the injury.
Graham hasn't missed a game since the 2015 season.
"The defense ... a lot of injuries," Packers quarterback Aaron Rodgers told reporters. "Offensively we lost Jimmy. But guys battled. Nobody gave up hope. We just didn't play well enough when we had to play well enough."
The Packers' next game comes against the Minnesota Vikings in an NFC North clash at 8:20 p.m on Sunday, Nov. 25 at U.S. Bank Stadium in Minneapolis.