The move follows a recommendation by Fifa's ethics judge Hans-Joachim Eckert as part of his findings into the Garcia investigation into the bidding for the two World Cups which were awarded 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 Michael Garcia, chairman of the investigatory chamber of the Fifa Ethics Committee," the organization said.
"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."
Fifa said the Swiss criminal prosecution authorities have the ability to conduct investigations under "application of criminal procedural coercive measures", which are not possible through the association's own organization.