1958–59 Cypriot Cup

The 1958–59 Cypriot Cup was the 19th edition of the Cypriot Cup. A total of 18 clubs entered the competition. It began on 9 April 1959 with the first round and concluded on 27 June 1959 with the final which was held at GSP Stadium. Anorthosis Famagusta won their 2nd Cypriot Cup trophy after beating AEL Limassol 1–0 in the final.

First round
1AEL qualified on draw

Quarter-finals
Συμπληρωματικός αγώνας