Government-run sports website Jit.cu says Mesa died Monday in the eastern city of Holguin, several days after he was hospitalized for a stroke.
Mesa, a southpaw, was born Dec. 6, 1966, in the eastern province of Santiago.
In 1996 he was runner-up in the bantamweight class at the Olympics in Atlanta. He won a gold medal at the Pan American Games in 1991, in Havana, and again four years later in Mar del Plata, Argentina.
His funeral is planned for Wednesday.