PAOK owner Ivan Savvidis then withdrew his team from the cup.
The Greek Cup semi-final between PAOK and Olympiakos was suspended after supporters clashed with riot police.
The final was played without fans at Athens' Olympic Stadium, and followed repeated match date delays.
The first-leg fixture had to be abandoned because of crowd trouble that started after PAOK had a penalty appeal rejected and riot police were called in to clear the pitch of missile-hurling fans.
Kontonis accepted a request by police to call off the game in the northern city of Thessaloniki because of a lack of available officers and a fear of violence.
Olympiakos, whose coach Marco Silva struck in the back by a plastic cup, came from behind after Mak's ninth minute opener, with Luka Milivojevic and Esteban Cambiasso netting for the visitors before halftime.
The match was called off in the 90th minute after fans broke onto the pitch to confront the police.
"In front of a stadium filled with 30,000 spectators these people do not fear God or the devil. Criminal prosecution against refereeing provoking violence should be taken," an angry Savvidis said in an interview with OTE-TV.
Robert Mak had given PAOK the lead in the match but two Olympiakos goals scored by Luka Milivojevic and former Leicester midfielder Esteban Cambiasso turned the match on its head.
GREEK football boffins have condemned crowd violence which caused PAOK Salonika and Olympiakos' cup game to be abandoned after a pitch invasion.
Olympiakos were knocked out of the Europa League last week after going down 3-1 on aggregate to Belgian side Anderlecht.
Olympiakos will be awarded an automatic 3-0 victory from the match - which was only the first leg - to take into the return leg on 6 April.
"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.
It was the second time in Greece this season that a match has been stopped. The Athens derby last November involving Panathinaikos and Olympiakos was called off due to violent clashes between fans and police before kick-off.
The violence, which erupted after a penalty was denied to PAOK in Wednesday evening's semi-final first-leg, also prompted Greece's deputy minister for sport Stavros Kontonis to recommend the suspension of all competitive football in the country.
The match will be rescheduled at a later date.
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The referee showed Mak a second yellow for diving and the decision sparked a mass pitch invasion from enraged home fans, who fought running battles with police before tear gas was used to disperse the crowd.
Olympiakos' official comment on Savvidis' statements was: "We do not deal with the delirium of Mr. Savvidis."
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Although fans were forced to stay away, the win came as a huge relief for supporters who remained loyal to the Athens club after they collapsed financially three years ago and clawed their way back from the amateur leagues.
Olympiakos' Super League game against Iraklis and champions Olympiakos, scheduled for Sunday, has also been postponed on the orders of the country's Deputy Sports Minister Stavros Kontonis after a request by police.
With Olympiakos 2-1 up in the match, PAOK were denied a late penalty to the fury of their supporters, who began to throw flares onto the pitch.
Jurgen Klopp's side came out on top on aggregate and there were unsavoury scenes in the stands as the final whistle approached
PAOK face a heavy fine as well as the possibility of being forced to play matches behind closed doors, while Olympiakos will now be awarded an automatic 3-0 victory to carry into the second leg on 6 April.
"In such matches a foreign referee should be used and if the federation doesn't have money for him, PAOK can bear the costs. For the first time in my life and watching all this I am ashamed that I connect myself with Greek football," Savvidis said.
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In an apparent reference to the migrant and economic crises now convulsing Greece, the EPO statement said it would "not allow football to be involved in games and goals that go beyond the controversies on the pitch and be burdened with the problems of an entire society."
AEK kept the Greek league champions in check, and Vargas picked out Pantalos Mantalos for a header in the 39th minute. Six minutes into the second half, he led a counter-attack that saw Rafik Djebour fire past goalkeeper Roberto.
Rather than needing to overturn just a one-goal deficit, PAOK will now need to score three times away from home to level proceedings in the tie.
Greek football has long been plagued by crowd trouble and PAOK can expect a hefty punishment, which will be more severe if the Salonika club carry out their threat of not turning up for the return leg in Athens on April 6.
Police said their staff had been depleted due to great numbers of officers being deployed to the northern Greek border town of Eidomeni, where thousands of migrants are gathered waiting to cross the border into Macedonia.
"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."
PAOK fans threw flares and clashed with riot police on the pitch before the match was stopped in the 90th minute with defending champions Olympiakos leading 2-1.
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Cup games were cancelled by the government in March following fan violence at a semifinal. It later reversed the decision under the threat of an international ban from FIFA.
THE average price for the May 18 Final is £550 on online company Ticketbis.
Violence broke out after the home side were denied a late penalty when Robert Mak, who had opened the scoring, appeared to be brought down by Olympiakos keeper Stefano Kampino.
"EPO condemns in the strongest possible way the extreme and unjustified, violent reactions which occurred before, during and after the cup match between PAOK and Olympiakos," the Greek FA said.
With Super League champions Olympiakos leading 2-1 in the 86th minute at a hostile Toumba stadium, PAOK were denied what looked like a clear penalty when Slovakia midfielder Robert Mak was felled by visiting keeper Stefano Kampino.