Photographs and footage showed Ivan Savvides, one of Greece's richest men, joining a pitch invasion in the closing minutes of a clash with Athens side AEK with what appeared to be a handgun strapped to his waist.
"We have decided to interrupt the championship ... It won't start again unless there is a clear framework, agreed by all, to move forward with conditions and rules," Greek Deputy Culture and Sports Minister Georgios Vassiliadis said.
Greek football has been plagued by pitch invasions and violence on and off the pitch. Authorities have repeatedly promised to clean up the game.
There was no immediate comment from Savvides or PAOK Salonika.
Vassiliadis said the suspension was indefinite until all involved agreed on a code of conduct and rules; "On our part much tighter rules on issues of security," he added.
The minister said "all necessary provisions would be taken" to make sure the suspensions did not affect the national side which has friendlies against Egypt and Switzerland later this month.
Savvides, accompanied by bodyguards, walked onto the pitch at Thessaloniki twice on Sunday, once wearing an overcoat, the second time with the coat off and his holster in plain view. He did not pull out a weapon.
He was held back at one point as he and others remonstrated with the referee, who had disallowed a goal from PAOK's Fernando Varela in the 89th minute. Up to then the match had been a goalless draw.
PAOK Salonika went on to be declared the winners after the referee reversed his decision two hours after the game and allowed the goal.
Police said they wanted to question Savvides for unauthorised entry to the pitch. The police statement did not mention a weapon. A police source said the PAOK boss was licensed to carry a firearm.