Instead, the country was given three months to put its house in order or risk a possible World Cup suspension.
Fifa had threatened to suspend Greece because of government interference in the affairs of the country's football association.
But after examining a detailed explanation submitted from Athens, the world governing body has decided to give the Greeks more time to comply with the rules.
A joint declaration signed by the Greek government, the Greek FA and Fifa agreed to set up a working party to try and resolve the present impasse.
Although the declaration was virtually impossible to decipher, Fifa said all potential sanctions were being put on hold.
The decision means that Greece's World Cup qualification programme, including a crucial home games with Albania and England at the beginning of June, will be unaffected provided there is an end to the dispute.
The domestic row centres around an amendment to the sports law in Greece which states that no sports official can hold office if he is accused of a serious crime.
The vice-president of the Greek FA, Victor Mitropoulos, has been accused of embezzlement.
Had the Greeks been suspended on Monday, the game against England almost certainly would have been postponed until next season.
Commenting on their decision, Fifa president Sepp Blatter explained why the Greeks had been given a stay of execution.
"It is our conviction that a constructive dialogue is the best way to find a solution to issues such as this," he said.