Swiss police earlier made pre-dawn arrests at the luxury Baur au Lac hotel in downtown Zurich, scene of raids on May 27 which sparked the FIFA corruption crisis.
The ministry says the two men, which it did not identify, are "suspected of accepting bribes of millions of dollars."
The arrests were made ahead of a FIFA executive committee meeting at 9 a.m. Swiss time (0800 GMT).
The bribes are linked to marketing rights for soccer tournaments in Latin America and World Cup qualifying matches, the ministry's statement said.
The U.S. Department of Justice has previously indicted two FIFA vice presidents among 14 soccer and marketing officials linked to bribes worth tens of millions of dollars for the Copa America tournament.
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