Cohen suffered the injury during Sunday's win over the Atlanta Falcons.
"You love the kid," Nagy told reporters. "He's worked hard to get to this point. We'll be in his corner and he'll be in our corner."
He rushed for 21 yards on two carries while also adding another 20 receiving yards before exiting Sunday's contest. The running back totaled over 2,600 yards from scrimmage during his first four seasons in the NFL.
Cohen recently agreed to a three-year contract extension worth up to $18.125 million. The deal includes $9.5 million fully guaranteed.
Chicago's rushing offense will likely lean on David Montgomery in Cohen's absence. Montgomery finished with 45 rushing yards in Sunday's victory.