Aliyev is a wealthy and powerful politician and businessman currently serving as his country's ambassador to Austria, where he was sent shortly after a scandal emerged involving Nurbank. He is living in what some have described as "luxury exile".
He has previously clashed with Nazarbayev over policy and the question of the president's succession.
Aliyev is married to Nazarbayev's eldest daughter, Dariga Nazarbayeva, a powerful politician in her own right who was previously seen by many observers as maneouvring to be her father's successor.
The criminal charges were announced by Bagdat Kozhakhmetov of the interior ministry in the Kazakh capital, Astana.
Kozhakhmetov read out only a police statement and did not take questions. Aliyev could not be reached for comment.
Nurbank's former CEO, Abilmazhen Gilimov, has accused Aliyev of staging his kidnapping and that of his deputy, a charge Aliyev has denied.
Government sources and analysts have said Aliyev's removal from the political scene could be linked to his falling out with the president in an oil-rich country where clan divisions dominate political life.
"It's a crisis situation... I don't think events like this make Kazakhstan a more investor-friendly place," Aidos Sarimov of the opposition-linked Altynbek Sarsenbaiuly think-tank said.
"Nazarbayev's main goal at the moment is to consolidate the elite ... and show everyone his rules of the game. It's a conflict of interests: both economic and political."
Nazarbayev's current presidential term expires in 2012. The country has never held an election judged free and fair by international monitors.
On Tuesday, Nazarbayev signed a law allowing him to stand for an unlimited number of terms, raising the prospect of becoming president-for-life.