It began on 14 January 1940 with the quarterfinals and concluded on 18 February 1940 with the replay final which was held at GSP Stadium.
AEL won their 2nd Cypriot Cup trophy after beating Pezoporikos 3–1 in the final.
In all rounds each tie was played as a single leg and was held at the home ground of one of the two teams, according to the draw results.
If extra time was drawn, there was a replay match.
The final abandoned after the first half due to rain.