The Swiss attorney general's office (OAG) said the probe opened in March and centres on allegations including bribery, fraud, criminal mismanagement and forgery of a document.
Prosecutors indicated that Al-Khelaifi, a powerful Qatari sports executive who is also head of beIN media, was under suspicion only for actions taken as the head of the sports media group, which operates on five continents.
The Qatar broadcaster issued a statement denying any wrongdoing while confirming French authorities had raided the company's Paris offices following a Swiss request.
"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," it said in a statement.
PSG, which grabbed headlines in August for its record signing of Brazilian superstar Neymar, is not implicated in the investigation.
Valcke, who was Sepp Blatter's right-hand man at FIFA, denied the allegations in an interview with French sports newspaper L'Equipe on Friday.
"They say there have been payments from Nasser to me in return for the sale of rights at a preferential rate. But I've received nothing from Nasser", he told the paper.
"There has never been an exchange between Nasser and me. Never."
Valcke left the Swiss attorney general's office on Thursday evening after being interviewed as a suspect and "disputes all the allegations", his lawyer told AFP.
"He came out free, there is no coercive measure against him nor any bail payment," Stephane Ceccaldi said.
The OAG said there was a third suspect in the case but identified him only as "a businessman in the sports rights sector".
Prosecutors said they had evidence indicating that Valcke "accepted undue advantages" from the businessman "in connection with the award of media rights for certain countries at the FIFA World Cups in 2018, 2022, 2026 and 2030".
The Swiss attorney general's office also alleged that Valcke had illegal dealings with "Nasser Al-Khelaifi in connection with the award of media rights for certain countries at the FIFA World Cups in 2026 and 2030".
The 2018 and 2022 World Cups will be played in Russia and Qatar respectively, while the 2026 and 2030 tournaments have not yet been awarded.
Valcke, a French national who also holds South African citizenship, was sacked from his post as FIFA's secretary general last year amid the corruption scandal that brought world football's governing body to its knees.
He became the subject of a separate Swiss corruption probe in March 2016 over criminal mismanagement during his FIFA tenure.
The previously disclosed allegations triggered his dismissal from FIFA and a 10-year ban from football.
Valcke was in Switzerland this week arguing an appeal at the Court of Arbitration for Sport in Lausanne, where he was trying to overturn the ban.
While Valcke was being questioned, authorities in France, Greece, Italy and Spain searched properties as part of the probe, Swiss prosecutors said, adding that no suspect in the case was currently in custody.
Unlike Valcke, whose career in world football is generally seen as finished, Al-Khelaifi's prominence in the sport has soared in recent months, especially following the Neymar signing.
PSG paid Barcelona a record 222 million euros ($264 million) for Neymar and Al-Khelaifi vowed that the acquisition would bring the Champions League title to the Paris side within two years.
PSG was bought by Qatar Sports Investments in 2011.
The new probe is the latest in a complex web of scandals that has rocked world football over the last two and a half years.
Dozens of corruption investigations are ongoing in Switzerland, the United States and elsewhere.
Many relate to the sale of broadcast and marketing rights, with FIFA insiders accused of taking kickbacks in exchange for sweetheart deals with broadcasters and promoters.
FIFA president Gianni Infantino, who took over from the disgraced Blatter last year, has vowed to clean up the game.
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