The proceedings follow an investigation by the prosecutor, Stefan Keller, into complaints regarding meetings between Mr Infantino, Swiss attorney general Michael Lauber and the chief public prosecutor of the Upper Valais, Rinaldo Arnold.
A statement from the Swiss federal council said Mr Keller has concluded that there are “indications of criminal conduct” in connection with those meetings.
The statement said that it concerns abuse of public office, breach of official secrecy, assisting offenders and incitement to these acts adding: "Additional criminal acts and the commencement of further proceedings remain reserved.”
It was confirmed in the same statement that Mr Keller is seeking approval from the relevant Swiss parliamentary committees to open criminal proceedings against Mr Lauber.
The statement concluded: “The presumption of innocence applies to attorney general Michael Lauber, FIFA president Gianni Infantino and chief public prosecutor Rinaldo Arnold.”
To meet with the head prosecutor or attorney general of Switzerland is perfectly legitimate and it’s perfectly legal.
Mr Lauber and Mr Infantino met twice in 2016, the year Mr Infantino was elected FIFA president.
Mr Infantino was asked about the case at last month’s FIFA Council meeting, and described the formal complaints against him as “absurd”.
“To meet with the head prosecutor or attorney general of Switzerland is perfectly legitimate and it’s perfectly legal,” he said.
FIFA has been approached for comment.