The 1939–40 Greek Football Cup was the fourth edition of the Greek Football Cup. The competition culminated with the Greek Cup Final, held at Leoforos Alexandras Stadium, on 2 June 1940. The match was contested by Panathinaikos and Aris, with Panathinaikos winning by 3–1.

Calendar

Qualification round

First round

Second round

Third round

Fourth round

Fifth round

Sixth round

Knockout phase

In the knockout phase, teams play against each other over a single match. If the match ends up as a draw, extra time will be played and if the match remains a draw a replay match is set at the home of the guest team which the extra time rule stands as well. That procedure will be repeated until a winner occurs. The mechanism of the draws for each round is as follows: The seeded teams are drawn against the unseeded teams.

Bracket

Round of 16

Quarter-finals

Semi-finals

Final