The 1936–37 Cypriot Cup was the third edition of the Cypriot Cup. A total of 7 clubs entered the competition. It began on 24 January 1937 with the quarterfinals and concluded on 28 February 1937 with the final which was held at GSP Stadium. APOEL won their 1st Cypriot Cup trophy after beating Enosis Neon Trust 2–1 in the final.