The name of the victim, who police said was stabbed in the chest at LP Field shortly after 8 p.m. local time, had not been released, The (Nashville) Tennessean reported.
Nashville police Capt. Ben Dicke said investigators had just started gathering information in the case.
It was Tennessee State University's 100th homecoming. A crowd of 31,765 had watched the Tigers beat Arkansas-Pine Bluff 40-13 to improve to 5-0 for the first time since 2001.