Basil Apokapes (or Apocapes) () was a Byzantine general of the 11th century. A descendant of the Apokapai family, an Armeno-Georgian noble clan, he was the son of the patrician Michael Apokapes or Abu K’ab, who had once served as a tent-guard for the influential Georgian Bagratid prince David of Tao (r. 966–1000) and then commanded the city of Edessa (modern-day Şanlıurfa, Turkey) under the Byzantine Emperor Michael IV the Paphlagonian (r. 1034–1041).