On the first play after Damarious Randall's interception set up Green Bay at Detroit's 25-yard line, Cook was unable to catch a deep crossing route that was thrown slightly behind him by quarterback Aaron Rodgers.
Cook, who had one catch for 15 yards, hobbled off the field and was examined by trainers before being taken to the locker room.
Cook missed most of the Packers' offseason program and the start of training camp after minor foot surgery. Neither Cook nor the team said which foot was injured.
Tight ends Richard Rodgers and Justin Perillo were used on Green Bay's opening drive of the third quarter, with the latter reeling in a 15-yard reception to set up a field goal.
Green Bay fullback Aaron Ripkowski (back) and Detroit safety Tavon Wilson (neck) also were injured on Sunday.