It began on 6 April 1940 with the semifinals and concluded on 11 May 1940 with the final which was held at GSP Stadium.
APOEL won their 2nd Cypriot Cup trophy after beating AEL 2–1 in the final.
In each round, each tie was played as a single leg and was held at the home ground of one of the two teams, determined by the draw results.
In the event of a drawn match, extra time was played.
If extra time also ended in a draw, a replay match was scheduled.