In a statement on August 8, HRW said that in Kazakhstan, Ablyazov would be at "serious risk of ill-treatment and would face a flagrant denial of his fair-trial rights."
It said the French authorities also should not send him to any country that might return him to Kazakhstan.
Ablyazov is wanted in Kazakhstan on embezzlement charges, which he says are politically motivated.
He fled the country in 2009.
He is also sought by Russia and Ukraine on related fraud charges.
He was arrested in southern France on July 31 at Ukraine's request.
Kazakhstan has no extradition agreement with France, but it has bilateral agreements with Russia and Ukraine.