Basil Apokapes (or Apocapes) (Greek: Βασίλειος Ἀποκάπης) 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).
In 1054, as patrikios and strategos, Basil Apokapes rallied the people of Manzikert and repulsed an attack by the Seljuks under Toğrül. Later, from 1059 to 1065, he served as archon (magistros and doux) of Paradounavon (modern northern Bulgaria, along the Danube) In 1064, together with the future emperor Nikephoros Botaneiates and his sons, he was defeated and captured by the Oghuz Turks who had crossed the northern Balkans, but the outbreak of epidemic soon decimated the invaders and the prisoners were recovered. After the defeat of Romanos IV by Andronikos Doukas in 1071, he seems to have been under the command of Philaretos Brachamios, a Byzantine general of Armenian heritage, who had established himself in Cilicia, and served him as a governor of Edessa from 1077 until his death in 1083.