The school did not give a cause of death but did say Bradshaw died away from campus and that authorities are "still gathering information surrounding the circumstances of his death."
Bradshaw was a walk-on receiver from St. Augustine, Florida who was recovering from offseason wrist surgery. He didn't play in the Buccaneers' spring season opener against Kennesaw State last week.
Charleston Southern coach Autry Denson called Bradshaw an "exceptional young man" who was committed to his football family.
Denson, in the school statement, added that after his surgery, Bradshaw was seen in the parking lot looking to take part in a football meeting he was excused from.
"I could go on and on about Joe," Denson said. "But what is most important is that we remember him for who he was."