The Broncos haven't revealed the extent of the injury, but NFL Network said tests earlier this week showed the partial tear, classified as a Grade 2 hamstring strain.
The team ruled Wilson out on Saturday and Brett Rypien was set to make the start against the Jets.
The report said a partial tear usually causes a player to miss multiple weeks. The Broncos are scheduled to play the Jacksonville Jaguars next Sunday in London and then have a bye in Week 9, so Denver could be targeting a return for Wilson on Nov. 13 at Tennessee.
Wilson, 33, injured his hamstring in Monday night's loss to the Los Angeles Chargers.