The government's move comes after several fans were injured in clashes in the stands and on the pitch during a Greek Cup semi-final between Kavala and Aris Salonica last Thursday.
Scenes of fans fighting running battles ensued after Aris fans ignored a ban on visiting supporters attending the game.
"Greeks have watched the latest troubles with rage and indignation," Bitsaxis told a news conference.
"We have spoken to all the institutions but unfortunately the dialogue and agreements have collapsed. All of this forces our hand to say that violence cannot be financed from Greek taxpayers."
Greek soccer has a poor record of crowd trouble and has been plagued by the problem again this season despite anti-violence advertising campaigns.
The suspension of funding is a significant step as it means professional clubs will be denied the revenues they receive from state-controlled betting agency OPAP, which are worth a reported 40 million euros per year.
"OPAP is not to finance this degradation," added Bitsaxis. "I now expect the Greek Football Federation and the leaders of professional football to undertake their responsibilities."
Only the Greek national team has escaped the stiff measure as they prepare for this year's World Cup in South Africa.
Bitsaxis said there would be plans for further measures including electronic ticketing and the creation of a code of disciplinary and administrative sentences, which could even mean clubs are closed down if there are repeated cases of violence.
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