
Prosecutors said they had discovered a dozen schemes, including one awarding the 2010 World Cup to South Africa.
Fourteen people are indicted, seven of whom were held in Zurich on Wednesday.
Fifa president Sepp Blatter is not among them. Fifa still intends to hold its presidential election on Friday.
Swiss prosecutors have also opened a separate investigation into the bidding process for the World Cup tournaments in 2018 in Russia and 2022 in Qatar.
BBC/RI