Montgomery, who sustained the injury during a 35-14 win over Chicago on Sept. 28, initially expressed optimism that he would play for the Packers (3-1) in their game against the Cowboys (2-2) on Sunday.
"I'm going to do my best to try to be out there (against the Cowboys)," the 24-year-old converted wide receiver said on USA Today's Clubhouse Live earlier in the week. "But of course, I have to be wary of risking something more serious. I don't want to puncture any internal organs. We all know how serious that can be."
Montgomery, who was limited in practice all week, has rushed 46 times for 152 yards and two touchdowns this season. He also has 18 receptions for 129 receiving yards and one score.
Jamaal Williams replaced Montgomery against the Bears and sustained a knee injury, leading to fellow rookie Aaron Jones serving as the feature back. Jones rushed for 49 yards and a touchdown on 13 carries.