"The EU's investigation of Gazprom, which has the potential to weaken Gazprom, has the potential to weaken Putin's regime," Kasparov told a democracy conference in Estonia.
"Both Russia's gas giant Gazprom and petroleum giant Rosneft are like a council in the Russian state, led by Putin oligarchs. Any weakening of Gazprom or Rosneft is a serious threat for Putin as it weakens his political and economical interests and that is why he takes it so seriously," Kasparov said.
"Putin recognises he has to been seen by people around him as someone who protects interests of all his gang," he added.
Putin has blasted Brussels for its challenge to Gazprom, a key supplier of gas to EU members, notably those that were under Soviet control until 1991.
The European Commission -- the executive body and competition watchdog of the 27-nation EU, with the power to impose hefty fines -- is investigating Gazprom's actions in eight member states.
In addition to Estonia, the countries allegedly affected by Gazprom's practices are Bulgaria, the Czech Republic, Hungary, Latvia, Lithuania, Poland and Slovakia.
The investigation centres on Gazprom's use of long-term contracts to lock in prices that are tied to that of oil -- a policy that often leaves its supplies far more expensive than those available on the open market.
Brussels insists that it simply wants fair treatment for all EU members, underlining that Gazprom charges west European nations less for gas.