According to the Office of the Attorney General of Switzerland, Mr Al-Khelaifi, who is also the president of French football club Paris Saint-Germain, is suspected of having bribed Fifa's former secretary general Jerome Valcke, who is also included in the proceedings together with an unnamed "businessman in the sports rights sector".
Swiss prosecutors said on Thursday they had opened a criminal investigation into former FIFA Secretary General Jerome Valcke and Nasser Al-Khelaifi, chief executive of Qatar's beIN Media, focused on corruption linked to World Cup broadcasting rights.
The office for the Swiss attorney general made the revelation on its official site on Thursday afternoon, and revealed that proceedings had been opened against the pair since March.
"At the same time, in cooperation with the competent authorities in France, Greece, Italy and Spain, properties were searched in various locations".
Al-Khelaifi is a key member of the organising committee for the FIFA World Cup in Qatar and was described by French newspaper L'Equipe as "the most powerful man in French football".
The Paris offices of BeIN Sports were searched on Thursday as part of a criminal probe against Valcke, which is part of FIFA's ongoing investigation into corruption in football.
Valcke is now serving a 10-year suspension for his alleged involvement in a scheme to profit from World Cup ticket sales.
BeIN Sports operates a global network of sports channel owned and operated by beIN media group.
Valcke was FIFA's secretary general under then-president Sepp Blatter from 2007 until he was sacked in January 2016.
Earlier this year, Khelaifi broke the world record for a player transfer fee by signing Brazilian footballer Neymar from Barcelona for €222 million. "The presumption of innocence applies".