According to Konstantopoulou, the court decided that Vinnik might face danger if extradited.
She added that he has been on hunger strike for four days.
On 20 December, Vinnik's lawyers appealed the decision by the Greek justice minister to authorize their client's extradition to France and then to the US and Russia over money laundering charges.
Vinnik began a hunger strike four days ago upon learning that he would be extradited. He previously went on a hunger strike for some 100 days last year in protest of the violations of his rights.
Russia, where he is wanted for a separate fraud charge, and France also seek his extradition. Vinnik has denied committing any criminal or administrative crimes.
In early November, Moscow provided Athens with additional materials related to the case. Following talks with his Greek counterpart, Nikos Dendias, Russian Foreign Minister Sergei Lavrov said that the only country Vinnik could be extradited to was Russia.