Per the Packers' official Twitter account, head coach Mike McCarthy announced Friday that Nelson has been ruled out for Sunday.
McCarthy added Nelson will travel with the team and be at AT&T Stadium.
Nelson was injured in the second quarter of the Packers' 38-13 win over the New York Giants last Sunday. He took a hard hit to the midsection from cornerback Leon Hall while trying to make a catch near the sideline.
Hall was not fined for the hit, per NFL Network's Ian Rapoport.
Rapoport reported Monday that Nelson suffered at least two fractured ribs, leaving him as a long shot to suit up for the Packers against the Cowboys.
We've played a lot of football together. You realize how important these opportunities are, how they don't come around every single year. We feel great about our team. Obviously, we feel better with 87 in the lineup. He's a classy guy and a great teammate. I was with him last night and the night before. He's staying positive and he's hopeful.
This was a terrific bounce-back season for Nelson after he missed all of 2015 with a torn ACL. The 31-year-old led the NFL with 14 touchdown catches while also leading the Packers in targets (152), receptions (97) and receiving yards (1,257).
The Packers will feel Nelson's absence, but there is a silver lining heading into Sunday: They scored all 38 points against the Giants after their star receiver was injured.
Rodgers has been incredible for the Packers with 19 touchdowns and no interceptions during their seven-game winning streak. He will have to continue that current roll without his top playmaker against the best team in the NFC if the Packers want to keep their season alive.