The lung injury wasn't initially disclosed by the Jets, who claim it won't affect Smith's timetable for return. He will be sidelined four to six weeks, according to coach Todd Bowles.
"Hopefully, he comes back sooner than that," Bowles said. "These types of things happen. It was a freak accident. We'll try to get him back as fast as we can, but we want him to be healthy."
Smith, a second-round pick from Ohio State, remained hospitalized for a second night. He averaged an FBS-leading 28.2 yards per catch for the Buckeyes the previous season. He recorded 33 catches for 931 yards and 12 touchdowns.
The injury happened when Smith, who made a catch on a deflected pass, got drilled in the back by safety Jaiquawn Jarrett. He got up slowly and was immediately taken to the locker room.
Smith, projected as the Jets' primary deep threat, is set to miss at least two preseason games. That will create an opportunity for other receivers, such as T.J. Graham, Chris Owusu and Shaquelle Evans.
The punctured lung was first reported by NJ Advance Media.