Violence erupted during Wednesday's game after a penalty was denied to PAOK.
PAOK's players and supporters were incensed by the decision, prompting an explosion of violence as large groups of fans rushed onto the pitch, hurling flares and missiles before being dispersed by riot police.
Greece's deputy minister for sport Stavros Kontonis had recommended the suspension of all competitive football in the country, but the Super League and the rest of the professional football divisions will continue.
“In view of...this mayhem in football grounds and a huge disturbance of the social peace and legal order in general, the government has decided to definitively cancel any process and match related to the Greek Cup as provided for by the law,” the government said in a statement.
“The government is closely monitoring developments and those who do not take seriously our policies should be aware that we will not hesitate to make further decisions on these matters."
AEK Athens were due to host Atromitos in the first leg of the other semi-final on Thursday. The home side released a short media statement saying the match had been cancelled.
The Hellenic Football Federation (EPO) had earlier condemned the ugly crowd violence, which occurred with Super League champions Olympiakos leading 2-1 in the 86th minute at a hostile Toumba stadium in Salonika.
PAOK were denied what looked like a clear penalty when Slovakia midfielder Robert Mak was felled by visiting keeper Stefano Kampino.
Hundreds of angry fans stormed the pitch and fought running battles with riot police in the closing minutes.
PAOK owner Ivan Savvidis immediately withdrew his team from the competition and called for the resignation of EPO president Giorgos Girtzikis.
It was the second time this season that a match in Greece has been stopped.
The Athens derby last November between Panathinaikos and Olympiakos was called off due to violent clashes between fans and police before kickoff.
Greek football has long been plagued by crowd trouble and PAOK can expect a hefty punishment.
(Editing by Toby Davis)
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