Kasparov, a critic of Russian President Vladimir Putin, was one of several witnesses whom Ablyazov’s lawyers wanted to call at the hearing in the central French city of Lyon.
Witnesses have never been called in extradition cases before and Judge Luc Fontaine on Friday declared that it was not allowed.
But he said witnesses could be called at a later stage if further information was needed.
One of Ablyazov’s lawyers Jean-Pierre Mignard said he would appeal against the decision.
"This is unacceptable, I regret the bad image given by the French justice system," he commented.
In Paris on Thursday Kasparov he "was not interested" in the details of the case but wished to tell the court that Ablyazov would face a “kangaroo court” in Russia.
After a spell as energy and trade minister, Ablyazov fell from grace with Kazakh President Nursultan Nazarbayev and founded an opposition party.
He is accused of embezzling billions while at the head of the BTA bank, which had interests in Ukraine and Russia, both of which have demanded his extradition.