Greece had indefinitely suspended matches after Savvides was filmed wearing a gun holster as he strode onto the pitch to protest about a PAOK disallowed goal against AEK Athens on Sunday.
The game was abandoned and later awarded to PAOK 1-0 following the controversial goal which had prompted the initial protests.
Savvides apologised for his actions in a club statement on Tuesday but the European Club Association (ECA) suspended the Greek side as a member with immediate effect.
"The suspension (of matches) does not bring anything," Superleague President Giorgos Stratos told reporters after meeting Deputy Culture and Sports Minister Georgios Vassiliadis.
"It creates a grave danger and we are possibly moving away from our aims and objectives."
Stratos said he had asked for the "quickest possible resumption" of matches but no date had been yet decided.
The 58-year-old Savvides, still sought by police for questioning over unauthorised entry to a soccer pitch, said he had no intention of causing harm to anyone.
"I want to apologise to PAOK fans, to Greek fans and to the global football community," he said in a club statement.
"I am sorry and I had no right to enter the pitch in such a way. I had no intention of clashing with anyone and I clearly did not threaten anyone."
Savvides was born in Georgia of Greek heritage. He has holdings in assets ranging from Thessaloniki port to tobacco and media companies, many of them in northern Greece.
The ECA, which represents European football clubs, suspended the Greeks indefinitely.
"ECA exists to protect the integrity and regularity of competitions and matches as well as the sporting values and principles on which European football is based," it said in a statement, condemning Savvides' action.
"The suspension remains valid until further notice and shall be reported to the ECA General Assembly in Rome on 27th March 2018."
Greek soccer has been plagued by pitch invasions and violence on and off the pitch for years and authorities have repeatedly promised to clean up the game.
However, attendances have dwindled and this season only four clubs in the 16-team top division have posted average attendances of more than 5,000 spectators per league game.
(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
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