A judge ruled that detaining him further was unjustified as the extradition procedure is expected to take a long time.
Under his bail conditions, Aliyev must not leave the country and must be available for the extradition procedure.
Earlier, he urged Austria not to extradite him to his homeland to face the charges, saying he would fear for his life if sent back.
Austrian police arrested him on an international warrant that also accuses him of running an organised crime network.
"Austria must not turn me over to a system where my life and the lives of my family are endangered," Aliyev was quoted as saying by an Austrian news-magazine shortly before his arrest.
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 says he thinks Nazarbayev acted because he had publicly challenged his father-in-law's dominance.