Valcke, whose job was to ensure the smooth running of FIFA and in particular its flagship World Cup tournament, was right-hand man to banned former president Sepp Blatter for nearly eight years.
He is suspected of criminal mismanagement and other offences, Michael Lauber's office said in a statement which added that the proceedings were in response to two criminal complaints against Valcke in connection with investigations by FIFA's ethics committee.
Searches were made on Thursday but the Frenchman was not arrested, prosecutors said. Valcke's U.S. lawyer Barry Berke declined to comment.
FIFA is mired in the worst crisis in its 112-year history, with corruption investigations under way in Switzerland and the United States.
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Several dozen people including senior football officials have been indicted in the United States while Swiss authorities have also opened a criminal investigation into Blatter, who has been banned for six years by FIFA's ethics committee.
Valcke joined FIFA in 2003 as marketing director but was fired in December 2006 for his part in botched sponsorship negotiations with credit card firms MasterCard Inc and Visa Inc.
Within months of that settlement, Valcke was not only back at FIFA but was at the helm of the administration as secretary general, answering directly to Blatter.
Valcke was widely credited with getting the 2010 and 2014 World Cup tournaments, held in South Africa and Brazil respectively, up and running in time after delays in the preparations.
Last month, FIFA ethics judge Hans-Joachim Eckert found Valcke guilty of misconduct over the sale of World Cup tickets, abuse of travel expenses, attempting to sell TV rights below their market value and destruction of evidence.
Eckert said that Valcke "acted against FIFA’s best interests and caused considerable financial damage to FIFA."
(Additional reporting by John Miller and Nate Raymond; editing by Andrew Roche)
