New York will be missing its No. 1 tight end due to a thumb injury and starting safety Minkah Fitzpatrick because of a groin issue when it faces Detroit on Sunday.
New York selected Cooper in the first round, and he will now miss significant time due to the injury, a source told NFL Network.
Sources say New York is expected to be without Cooper for multiple weeks after an MRI revealed a sprain, prompting the team to add veteran receiver depth.
New York will be without former All-Pro safety Minkah Fitzpatrick due to a groin injury as the team continues its record-setting stretch without an interception.
Both New York NFL franchises began their seasons with victories, according to ESPN, marking the first time in more than 15 years that the Jets and Giants have started 1-0 together.