The 6-foot-4, 300-pound Winn suffered the injury during an inside run drill at about 10:23 a.m.
An athletic trainer appeared to examine Winn's right knee on the sideline for about five minutes, then summoned the cart. Winn held his head down as the cart transported him from the outdoor practice fields and into the field house.
The severity of the injury is unknown. Coach Mike Pettine is expected to provide an update once practice ends at about noon.
The injury occurred less than 24 hours after Pettine praised Winn for his work this offseason.
"I think he has had one of his better offseasons," Pettine said.