They have seized information about a contract disclosed in the Panama Papers that was signed by former Uefa general secretary Gianni Infantino, now head of the global football body Fifa.
Infantino has denied wrongdoing, while Uefa says it is helping police.
Meanwhile, a Fifa ethics committee official named in the papers - Juan Pedro Damiani - has resigned.
Leaked documents suggest the Uruguayan and his firm provided legal assistance for at least seven offshore companies linked to Eugenio Figueredo.
A former Fifa vice-president, Figueredo was among 14 people arrested in Zurich last May as part of the US inquiry.
The office of the Swiss attorney general said the search of Uefa offices in Nyon was part of "ongoing criminal proceedings" and had been launched because of "suspicion of criminal mismanagement and ... misappropriation".
It added that criminal proceedings "are in connection with the acquisition of television rights and are at present directed against persons unknown".
While at Uefa, Infantino co-signed a television rights deal in 2006 with two businessmen who have since been accused by the FBI of bribery.
Cross Trading - owned by Hugo Jinkis and his son Mariano - bought TV rights for Uefa Champions League football in 2006 for $111,000 (£78,000) and immediately sold them to Ecuadorian broadcaster Teleamazonas for $311,170 (£220,000).
Cross Trading also paid $28,000 (£20,000) for the rights to the Uefa Super Cup, selling those to Teleamazonas for $126,200 (£89,000).
The contract came to light after 11 million documents were leaked from Panamanian law firm Mossack Fonseca.
Uefa initially denied doing business with anyone indicted by the FBI.
It has since told the BBC that the TV rights were sold to the highest bidder in an open and competitive tender process.
It also stressed it has been "conducting a review of its various commercial contracts" following the US indictments in May 2015.
Uefa has backed Infantino, describing him as "an outstanding member of Uefa staff for many years" and "a man who has always acted with complete professionalism and integrity".
Infantino, who left Uefa after being elected Fifa president on 26 February, said he welcomed "any investigation into this matter".
The Swiss-Italian added: "If my determination to restore football's reputation was already very strong, it is now even stronger. It is in my interest and in the interest of football that everything should come to light."
A senior Fifa source has told the BBC the 2006 deal should be examined by Fifa's ethics committee.
There is no evidence to suggest Infantino - then Uefa's director of legal services - received a bribe relating to the contract with Cross Trading and no suggestion Teleamazonas was in any way complicit in any wrongdoing.
Cross Trading also has links to Damiani.
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