The proceedings relate to Qatari-owned beIN Media Group, of which Al-Khelaifi is chief executive, being awarded the TV rights for the 2026 and 2030 World Cups.
Federal prosecutors say the new proceedings are connected with an ongoing investigation which the Office of the Attorney General of Switzerland (OAG) opened last year against former FIFA secretary general Jerome Valcke in relation to "various acts of criminal mismanagement."
The proceedings also relate to "suspicion of bribery of private individuals ... fraud ... and forgery of a document."
In a statement issued Thursday, the OAG said new proceedings have been opened "primarily on the basis of findings obtained by the OAG in this earlier proceeding."
The statement added: "It is suspected that Jerome Valcke accepted undue advantages from a businessman in the sports rights sector in connection with the award of media rights for certain countries at the FIFA World Cups in 2018, 2022, 2026 and 2030 and from Nasser Al-Khelaifi in connection with the award of media rights for certain countries at the FIFA World Cups in 2026 and 2030."
Prosecutors said the new investigation was opened in March 2017 and that Valcke was interviewed in Switzerland as a suspect.
Prosecutors also said it was working with authorities in France, Greece, Italy and Spain, where properties had been searched.
Valcke was banned from football for 10 years for his alleged involvement in a scheme to profit from World Cup ticket sales. The Frenchman has appealed against the sanction.
Al-Khelaifi, 43, was appointed PSG chairman and chief executive in 2011 and was instrumental in the French club's acquisition of Neymar from Barcelona in August for a world record fee.
"Following a request by the office of the Attorney General of Switzerland (OAG), the beIN SPORTS offices in Boulogne-Billancourt (France) were searched this morning," said a beIN statement.
"The employees on site cooperated with the authorities until the end of the search.
"BeIN Media Group refutes all accusations made by OAG. The company will fully cooperate with the authorities and is confident as to the future developments of this investigation."
FIFA said in a statement that it "fully supports the investigation conducted by the Swiss Office of the Attorney General."
The world governing body added: "FIFA has constituted itself as a damaged party in this investigation, in line with the applicable provisions of Swiss procedural law."
PSG and Valcke were not immediately available for comment.
"No one has been on remand," added the OAG statement. "The presumption of innocence applies."