Jones, 19, of Smyrna, Tenn., was involved in a non-contact drill when he fell to the ground about 4 p.m. Wednesday. He was unresponsive to actions by team trainers and was taken to Baptist Hospital in Nashville where he was pronounced dead.
"This is a very tragic day for our entire Tennessee State University community and we are devastated by the sudden passing of this young man," Athletic Director Teresa Phillips said in a statement.
"Our thoughts and prayers are with his family during this very difficult time. Our university and our football team are hurting as we feel the loss of one of our own. As a team and a family, we will grieve alongside the family and do everything we can to help support the family through this very difficult time."
School officials said they were unaware of any pre-existing conditions that may had led to Jones' death.
Jones was a walk-on to the team and hadn't appeared in a game this season.
Tennessee State (8-2) is off this week and completes its regular season Nov. 17 at Tennessee-Martin.