The Swiss attorney-general's (OAG) office said the search in Nyon, Switzerland, was part of "ongoing criminal proceedings" and had been launched because of "suspicion of criminal mismanagement and ... misappropriation".
"The OAG's criminal proceedings are in connection with the acquisition of television rights and are at present directed against persons unknown, meaning that for the time being, no specific individual is being targeted by these proceedings," it added.
Infantino, elected FIFA president in February, said in a statement issued by the football body that he welcomed any investigation into the matter. He said on Tuesday he was "dismayed that his integrity was being doubted".
Reports from multiple news organisations, citing a leaked document from the so-called Panama Papers, said on Tuesday UEFA sold broadcast rights for 2006-09 Champions League matches to Argentine businessmen Hugo and Mariano Jinkis, owners of Cross Trading.
These reports said the pair resold the rights to Ecuadorean broadcaster Teleamazonas for three times as much, though UEFA said it had no knowledge of such a deal.
UEFA has confirmed that Infantino, who was working for UEFA at the time, was one of two of its officials who signed the contract. UEFA has denied any wrongdoing by itself or Infantino.
"UEFA can confirm that today we received a visit from the office of the Swiss Federal Police acting under a warrant and requesting sight of the contracts between UEFA and Cross Trading/Teleamazonas," UEFA said in a statement.
"Naturally, UEFA is providing the Federal Police with all relevant documents in our possession and will cooperate fully."
Hugo and Mariano Jinkis are among several dozen football officials who were last year indicted in the United States as part of a huge corruption scandal which has swept the game and thrown FIFA into turmoil.
Infantino was elected as FIFA president to try to lead the federation into a new, scandal-free era.
'Football's reputation'
"It is in my interest and in the interest of football that everything should come to light," Infantino said in the statement issued by FIFA on Wednesday, adding that "all contractual matters were conducted properly by UEFA".
"If my determination to restore football's reputation was already very strong, it is now even stronger," he said.
The document was part of the 11 million that were leaked from the Panamanian law firm Mossack Fonseca in what have become known as the Panama Papers. The law firm has denied wrongdoing.
In a separate statement, UEFA said the rights were sold to Teleamazonas after an "open, competitive, tender process" conducted by TEAM, its exclusive agent".
TEAM is UEFA's marketing partner which conducts the negotiations for the sale of broadcast rights.
"We can also add that the offer made by Teleamazonas was very much the 'going rate' for this category of rights in comparable markets in Latin and Central America," UEFA said.
UEFA said there had been a tender, competing offers and it would have been "unusual" if it had not accepted the Teleamazonas offer which it said was the best one.
UEFA added that Cross Trading had the exclusive mandate to buy sports TV rights in Europe on behalf of Teleamazonas and said that, at the time, there was no reason to believe there was anything suspicious about it.
Referring to the alleged resale by Cross Trading, UEFA said it has "no knowledge of any bilateral or private financial arrangements between Cross Trading and Teleamazonas. Neither UEFA nor TEAM have ever seen any contract or agreement between Cross Trading and Teleamazonas".
It added that anything suspicious about any agreement between the two companies should be investigated by the appropriate authorities.
"There is, we repeat, absolutely nothing in this story which could in any possible way serve to undermine the integrity of either UEFA or Gianni Infantino," UEFA said.
In another development, FIFA's ethics committee said Juan Pedro Damiani, a member of its judgement chamber who had been placed under a preliminary investigation, had resigned.
On Sunday, the committee said it was looking into a possible business link between Damiani and fellow Uruguayan Eugenio Figueredo, one of the indicted officials, although it did not give details or say why the relationship might be problematic.
Damiani, a member of the committee since 2006, has denied wrongdoing and said his law firm had ended its professional link with Figueredo as soon as the FIFA issue came to light.
