Mladineo was arrested in Zagreb on 22 November.
He is kept in detention for fear that he might tamper with witnesses, according to a decision of the Zagreb County Court's investigating judge.
The lawyer announced an appeal against his client's detention in custody.
The investigation in the Fimi Media case has established that about a dozen people, including former Prime Minister Ivo Sanader, were involved in that wrongdoing, embezzling at least HRK 80 million.