After months of probes following raids in Zurich which led to the indictment of more than a dozen top officials, Swiss investigators said their attention had now turned to actions carried out by Blatter and Platini.
"Swiss criminal proceedings against the President of FIFA, Mr. Joseph Blatter, have been opened on September 24, 2015 on suspicion of criminal mismanagement...And - alternatively - misappropriation," said a statement from Switzerland's attorney general's office (OAG).
Swiss prosecutors said Blatter was being investigated over the 2005 sale of World Cup television rights to the Caribbean Football Union, then run by former ally Jack Warner, a deal which had been "unfavourable for FIFA".
Blatter was also suspected of a "disloyal payment" of two million dollars to Platini in February 2011 allegedly made for work the Frenchman carried out for FIFA between 1999 and 2002, before he was elected as head of UEFA.
Swiss authorities said Blatter was questioned as "a suspect".
The statement added that Platini had been questioned "as a person called upon to give information".
Blatter's lawyer Richard Cullen said in a statement that the FIFA boss was co-operating with Swiss authorities and that a review of the evidence would show "no mismanagement occurred".
Platini meanwhile defended the payment issued to him in 2011, which was made three months before the Frenchman announced he would not challenge Blatter for re-election during that year's race for the FIFA presidency.
"I was pleased to have been able to clarify all matters relating to this with the authorities.
