It said Blatter was interrogated after a meeting of FIFA's executive committee in Zurich, and authorities carried out a search at the organization's headquarters on Friday.
"The office of the FIFA President has been searched and data seized," the office of the attorney general (OAG) said.
It was the first time that authorities investigating corruption in the world's most popular sport had pointed the finger directly at Blatter, the 79-year-old Swiss who has run its powerful governing body for the past 17 years.
He has denied wrongdoing and his U.S. attorney said he was cooperating with the Swiss probe.
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The life and times of Sepp Blatter
Blatter to cooperate with Swiss probe
The lawyer for FIFA president Sepp Blatter says his client will cooperate with Swiss authorities investigating whether he made corrupt payments.
The lawyer, Richard Cullen, was quoted by The New York Times on Friday as saying that the evidence would show that a contract in question with the Caribbean football union in 2005 was negotiated properly.
"Certainly no mismanagement occurred," Cullen told the Times.
"Mr Blatter is cooperating and we're confident that when the Swiss authorities have a chance to review the documents and the evidence they will see that the contract was properly prepared and negotiated by the appropriate staff members of FIFA who were routinely responsible for such contracts."
The investigation into Blatter also includes an alleged "disloyal payment" of 2 million Swiss francs to the president of European football's governing body, Michel Platini.
The contract is reportedly on the sale of TV rights to the Caribbean and involves former FIFA vice-president Jack Warner of Trinidad and Tobago, whose extradition US authorities are seeking in connection with their own probe.
The FBI, which has a number of ongoing investigations into alleged corruption by football officials, had no comment over the developments in Switzerland.
Kelly Langmesser, an FBI spokesman in New York, told DPA it wouldn't be appropriate for the FBI to comment on an investigation launched by another law enforcement authority.
"It's over for him now'
A source close to FIFA said that as Blatter has not been arrested, charged or indicted, it would probably be for him to decide whether he stays in his post until February, when he is due to step down.
However, the source said: "It is over for him now, it is finished."
The news of the investigation broke shortly after FIFA had abruptly canceled a Blatter press conference at 15 minutes' notice, offering no explanation.
He had been due to speak for the first time since his number two, Jerome Valcke, was suspended last week following accusations regarding ticket sales at the 2014 World Cup in Brazil. Valcke denied the allegations.
In a sign of concern over the implications of the deepening investigation, Russia was quick to say that it would not affect its hosting of the 2018 World Cup, one of the biggest and most lucrative events in sport.
FIFA's awarding of the 2018 and 2022 competitions to Russia and Qatar is one of the strands under scrutiny from U.S. and Swiss authorities investigating corruption in the organization -- a worry for tournament sponsors such as McDonald's Corp, Coca-Cola and Visa.
The scandal exploded in May, when 14 soccer officials and sports marketing executives were indicted. Seven were arrested by Swiss police in a dawn raid on a five-star Zurich hotel.
Platini testifies
The Swiss OAG said Blatter had been questioned by its representatives, and that Michel Platini, the former French midfield soccer star who runs European soccer body UEFA, had also been asked to give information.
Platini is favorite to win the election to replace Blatter when he steps down in February. Blatter once described their relationship as "like father and son", but it broke down irretrievably earlier this year when Platini urged him to quit.
A Swiss law enforcement source said that Platini had provided Swiss prosecutors with evidence against Blatter and was not regarded as a target of investigators at this point.
Swiss investigators have been putting together their case against Blatter for some time, a law enforcement official said.
The official said Blatter is not in custody and is free to travel, though he has largely avoided leaving Switzerland since May.
According to the Swiss criminal code, Blatter could, if convicted, face a custodial sentence of up to five years depending on the circumstances of the offence.
The OAG statement said he was suspected of a "disloyal payment" of 2 million Swiss francs ($2.05 million) to Platini at the expense of FIFA, allegedly made for work performed between January 1999 and June 2002.
The payment was executed in February 2011, the OAG said. It did not say why the payment was "disloyal" or what became of the money.
Platini said in a statement: "Regarding the payment that was made to me, I wish to state that this amount relates to work which I carried out under a contract with FIFA and I was pleased to have been able to clarify all matters relating to this with the authorities."
Caribbean contact
The OAG said it also suspected Blatter of signing a contract in 2005 with the Caribbean Football Union (CFU), then headed by Trinidadian soccer baron Jack Warner, that was unfavorable for FIFA and had "violated his fiduciary duties", or duties of trust.
Richard Cullen, a U.S. lawyer for Blatter, said: "Mr. Blatter is cooperating and we are confident that when the Swiss authorities have a chance to review the documents and the evidence they will see that the contract was properly prepared and negotiated by the appropriate staff members of FIFA who were routinely responsible for such contracts, and certainly no mismanagement occurred."
According to a FIFA document seen by Reuters, the 2005 agreement required that FIFA be paid both up-front “rights fees” and a 50 percent share of revenue from "broadcast sponsorship and commercial airtime opportunities".
But according to the document -- a July 2011 letter signed by FIFA’s now suspended secretary general Valcke -- Warner's CFU did not make any of the payments that were due.
FIFA said in a statement on Friday that it had been cooperating with the Swiss authorities since May and had complied with all requests for documents, data and other information. "We will continue this level of cooperation throughout the investigation," it said.
A spokeswoman for U.S. prosecutors declined to comment. The FBI said it did not comment on other agencies' investigations.
Damian Collins, a British member of parliament and co-founder of campaign group NewFIFANow, said the opening of the criminal probe against Blatter and the questioning of Platini showed the need to overhaul soccer's governing body under an independent interim administration.
"The house of FIFA is tumbling down," he said.
Blatter has survived a series of scandals during his term in office, including widespread accusations that Qatar bought the right to stage the 2022 World Cup. Qatar has always denied any wrongdoing.
Despite widespread calls for Blatter's resignation when the U.S. indictments were issued in May, he refused to withdraw his candidacy for a fifth term at the helm of FIFA. He was duly re-elected, telling delegates: "Football needs a strong and experienced leader."
As the scandal reverberated around the world and his position became untenable, he announced only days later that he would step down, though for the time being he remains in office until the election of his successor.
