It follows a recommendation by FIFA's ethics judge Hans-Joachim Eckert as part of his final summary of the Michael Garcia investigation into the controversial awarding of the World Cups to Qatar and Russia.
"This criminal complaint has been lodged today," FIFA said in a statement.
"The subject of the criminal complaint is the possible misconduct of individual persons in connection with the awarding of the hosting rights of the 2018 and 2022 World Cups investigated by Garcia, chairman of the investigatory chamber of the FIFA Ethics Committee.
"In particular there seem to be grounds for suspicion that, in isolated cases, international transfers of assets with connections to Switzerland took place, which merit examination by the criminal prosecution authorities."
Garcia, a former New York federal prosecutor, spent 18 months investigating the bidding process for the two tournaments.
FIFA last week published a resume of Garcia's report and cleared Qatar and Russia of corruption and ruled out a re-vote for the tournaments despite widespread allegations of wrongdoing.
Garcia slammed that version of his report as "incomplete and erroneous" has lodged an appeal.
The Garcia report will be handed over to the attorney general's office by Eckert but he and Blatter remain adamant the report cannot be published.
Blatter told FIFA's website: "There is no change to judge Eckert's statement that the investigation into the bidding process for the 2018 and 2022 FIFA World Cups is concluded.
"The matter will now also be looked at by an independent, state body, which shows that FIFA is not opposed to transparency."
Asked about the publication of the report, he added: "If FIFA were to publish the report, we would be violating our own association law as well as state law. The people who are demanding in the media and elsewhere that FIFA publish the report are obviously of the opinion that FIFA should or must ignore the law in this regard."
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