Milinkevich spokesman Pavel Mazheyka says Milinkevich was held a few hours and later released.
He has been charged with leaving the country without proper documents and faces a possible fine.
Milinkevich is a leading opposition figure who ran against Belarusian President Alyaksandr Lukashenka in a March presidential election.
Speaking in Riga on November 28, Bush said Lukashenka's government "offends the conscience" of Europe and the United States.
Western governments have characterized Lukashenka -- who is regularly criticized for rights abuses -- as the last dictator in Europe.
(Interfax, AFP, AP)