Police detained Gia Djokhtaberidze, saying he had ignored an order by the prosecutor's office to not leave Georgia pending an outcome of an investigation into tax evasion charges. Djokhtaberidze is a shareholder in Magticom, Georgia's biggest cellular communications company.
The presidency's statement said Shevardnadze "will not suffer the fate" of his son-in-law.
Saakashvili led opposition protests that toppled Shevardnadze last November. He has pledged to crack down on corruption.