The Swiss attorney general's office (OAG) said the inquiry started in March and centres on allegations including bribery, fraud, criminal mismanagement and forgery of a document.
Prosecutors indicated that Al-Khelaifi, 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.
Valcke, who was second in command to longtime Fifa head Sepp Blatter, denies the allegations. He left the Swiss attorney general's office on Thursday after being interviewed as a suspect.
"He came out free. There is no coercive measure against him nor any bail payment," said his lawyer Stephane Ceccaldi.
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 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 venues of the 2026 and 2030 tournaments have not yet been decided.
Valcke was sacked from his post as Fifa's secretary general last year and banned from football related activities for 10 years amid the corruption scandal that rocked world football's governing body.
Valcke is appealing to the Court of Arbitration for Sport in Lausanne to overturn the ban.