Separately, Swiss prosecutors have launched a criminal case into the 2018 and 2022 football World Cup bids.
The suspects, who include a FIFA vice-president, allegedly accepted bribes worth $150 million over 20 years.
FIFA members are due to vote on May 29 in a presidential election when incumbent Sepp Blatter is seeking a fifth term.
However, Sepp Blatter is not understood to be one of those arrested.
Prince Ali Bin al-Hussein of Jordan – Sepp Blatter’s rival for the FIFA presidency – described the development as “a sad day for football”, but withheld from commenting further.
FIFA’s Zurich headquarters has also been raided, with documents seized, Swiss prosecutors say.
Among those arrested in Zurich are: Jeffrey Webb – head of the confederation for North and Central America and the Caribbean, CONCACAF; Jack Warner, former FIFA vice-president; Costa Rica’s national football chief Eduardo Li, who was due to join FIFA’s executive committee on May 29; Uruguay’s Eugenio Figueredo, president of South American football governing body CONMEBOL; Brazil’s Jose Maria Marin, a member of FIFA’s club committee.
Police were seen carrying Jose Maria Marin’s suitcase and some of his possessions in plastic bags.
Several officials have already pleaded guilty, the US Department of Justice says. These include Charles Blazer, the former head of CONCACAF, who was previously on the FIFA executive committee.
A FIFA spokesman said the governing body was seeking to clarify the situation.
The Swiss Federal Office of Justice (FOJ) said in a statement on May 27 that US authorities suspected the officials of receiving $150 million worth of bribes since the early 1990s for football tournaments in Latin America.
The crimes were agreed to and prepared in the US via US bank accounts, the statement adds.
Swiss authorities can immediately approve the extradition, it continues.
In a separate move, prosecutors opened criminal proceedings “against persons unknown on suspicion of criminal mismanagement and of money laundering in connection with the allocation of the 2018 and 2022 football World Cups,” said a statement from the Swiss attorney-general.
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