The first-leg fixture had to be abandoned in the 90th minute because of crowd trouble that started after PAOK - trailing 2-1 at the Toumba Stadium - had a penalty appeal rejected and a player sent off.
The home side were denied what looked like a clear penalty when Slovakia midfielder Robert Mak - who was subsequently red carded for his protestations - was felled by visiting keeper Stefano Kampino. Hundreds of angry fans stormed the pitch.
Riot police were called in to clear the pitch as PAOK supporters lit dozens of flares and fireworks and threw them on to the field.
PAOK owner Ivan Savvidis immediately withdrew his team from the competition and called for the resignation of Hellenic Football Federation president Giorgos Girtzikis.
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 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," a government statement read.
"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."
The second semi-final was scheduled to be between AEK and Atromitos, with the hosts confirming via a media statement that the match had been cancelled.
