During his club career, Barison played for S.S.C. Venezia, Genoa C.F.C., A.C. Milan, U.C. Sampdoria, A.S. Roma, and S.S.C. Napoli. He was a key figure in Milan winning the 1962–63 European Cup, scoring six goals during their cup run, however he was dropped for the final in favour of Gino Pivatelli.