Savvidis, who is one of the country's richest men, was unhappy with the officials' decision to disallow his side a late goal and entered the field with the firearm.
Players made their way off the pitch and, after a two-hour wait, the meeting with AEK Athens was postponed on police advice.
In the wake of the alarming incident, Greek Deputy Culture and Sports Minister Georgios Vassiliadis has announced that no top-flight matches will go ahead until further notice.
"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," he said.
PAOK are third in the Greek top flight and would have moved within a couple of points of leaders AEK Athens with victory on Sunday.