Aliyev again denied all wrongdoing, saying, "I'm not resisting an investigation. I have nothing to hide."
The arrest of Aliyev, who declared he wanted to run for president in 2012, is a new chapter in the struggle for power and influence in oil-rich Kazakhstan where clan divisions and family connections play a central role in politics.
Nazarbayev ordered police to investigate his son-in-law last week, seized some of his media assets and sacked him from his position as Kazakh ambassador to Vienna.
An international arrest warrant for Aliyev was issued on Monday and he lost his diplomatic immunity a day later.
Nazarbayev's move came days after he signed constitutional amendments allowing him to stay in office for life.
Aliyev told profil he thought Nazarbayev acted because he had publicly challenged his father-in-law's dominance.
"The president told me over and over: 'This is my country. Everyone does what I want, and you are the only one who does not obey me,"' he said, accusing Nazarbayev of tarring the country's reputation.