Aliev, who is married to the Kazakh president's eldest daughter, is wanted in connection with the kidnapping of two officials of a Kazakh bank, Nurbank, in January. Aliev denies the charges.
Relatives of the two Nurbank officials told RFE/RL earlier this year that Aliev had kidnapped the two and beat them to force them to sell the property housing the bank's headquarters. One of the managers is still missing.
Interior Ministry spokesman Bagdat Kozhakhmetov said Aliev is also being investigated for links to organized criminal groups and a number of financial crimes. Kozhakhmetov said a group of Kazakh investigators, including a deputy prosecutor-general, have already left for Vienna.
Aliev was dismissed as ambassador to Austria on May 26. He earlier accused Kazakh President Nursultan Nazarbaev of trying to silence him after he announced his intention to run for president of Kazakhstan.