The match was due to be held behind closed doors due to crowd violence that has blighted this season's competition.
However, a nationwide 48-hour strike by various trade unions that began on Friday meant the police did not have the resources to oversee the game.
"By a decision from the Deputy Minister of Culture and Sport Mr Stavros Kontonis, the Greek Cup final has been postponed following a request from the police and the recommendation of the anti-violence committee," said a government statement.
No new date for the match has been announced.
The postponement is the latest twist in what has become a farcical Greek Cup saga.
Kontonis cancelled the competition after the first leg of the semi-final between PAOK Salonika and Olympiakos on March 2 was abandoned due to a pitch invasion.
Fans also hurled flares and missiles before being dispersed by riot police.
Kontonis reversed his decision last month after ruling body FIFA and European counterpart UEFA warned the country would be suspended from international football if the Greek Cup did not resume.
The competition restarted with the remaining games played behind closed doors for security reasons.
PAOK then failed to show up for the second leg of their semi-final and were punished with a heavy fine and a three-point points deduction that will take effect from the start of the 2016-17 league season.
(Editing by Tony Jimenez)
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