The competition was called off after the first leg of the semi-final between PAOK Salonika and Olympiakos Piraeus was abandoned on March 2.
FIFA and European football's governing body UEFA sent a joint letter to the Greek authorities on Friday requesting they reverse the cancellation within two weeks, describing the decision as disproportionate.
"In case of non-compliance, the relevant FIFA bodies would consider sanctions," said FIFA in a statement following an executive committee meeting.
Sanctions could include the suspension of the Greek federation, preventing Greek clubs from playing in European club competitions while the national side would also be barred from playing.
Violence erupted during the game after a penalty was denied to PAOK.
Their players and supporters were incensed by the decision, prompting an explosion of violence as large groups of fans rushed on to 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 haven continued.
It was the second time this season that a match in Greece has been stopped. The Athens derby in November between Panathinaikos and Olympiakos was called off due to violent clashes between fans and police before kickoff.
In another decision on Friday, FIFA's executive committee agreed to allow an experiment with extra substitutes during the Olympic Games, women's Under-20 World Cup and Club World Cup tournaments this year.
FIFA said a fourth substitute, in addition to the usual three, could be used in matches that went to extra-time. This followed a recommendation made by football's rule-making body IFAB earlier this month.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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