Smith was diagnosed by team doctors at the facility and was kept out of practice. Coach Robert Saleh didn't mention the accident at his news conference before practice.
The Jets (0-3), who face the Tennessee Titans (2-1) on Sunday, probably will be without Smith and rookie Elijah Moore (concussion) at wide receiver. Jamison Crowder (groin), who was out the past three games, is "trending" toward playing, Saleh said.
It would give the Jets four receivers for the game, opening a possibility for 2020 second-round pick Denzel Mims to be active. Mims was a healthy scratch the past two games.
Smith, 24, who signed with the Jets as an undrafted free agent in 2019, is their No. 5 receiver and the starting gunner on the punt team. He has 20 career catches for 227 yards, including two for 48 yards this season. He played his college ball at Boston College, starting out as a quarterback before switching to wide receiver.