Last week, Nursultan Nazarbayev, the president, ordered the police to investigate his son-in-law on suspicion of kidnapping two senior employees of Nurbank, a Kazakh bank in which Aliyev is a major shareholder, in January.
On Monday, Kozhakhmetov said Aliyev was accused of running a organised crime network in the Central Asian state, in addition to the abduction charges.
"The head of this criminal group ... is currently Rakhat Aliyev," he told reporters.
The investigation into Aliyev was launched shortly after Nazarbayev had signed constitutional amendments which allow him to stay in office for the rest of his life.
Aliyev, the husband of Nazarbayev's eldest daughter, Dariga, first fell out with the president in November 2001 and armed security forces were dispatched to search for him in the country's second city, Almaty.
The two men eventually worked out their differences and Aliyev was dispatched to serve as ambassador to Austria in 2002.
He returned to the post of deputy foreign minister in 2005 but was again dispatched to serve in Austria in the wake of the disappearance of the Nurbank officials.
After he was accused of being involved in the kidnapping Aliyev revealed that he had told Nazarbayev of his political ambitions.
"Several months ago I told Nursultan [Nazarbayev] that I had taken the decision to stand for the presidency at the next elections in 2012 ... Soon after this conversation the Nurbank robbery saga began," he said.
Aliyev's whereabouts have been unclear since he was sacked from the post of ambassador to Austria on Saturday.