Ministry spokesman Lars Knuchel confirmed the warrant after a newspaper published the document issued by an examining magistrate in the Swiss canton (region) of Vaud, where the activist Kazem Rajavi was assassinated in 1990.
The affair "is still in the order of business (between Berne and Tehran) since 1990", Mr Knuchel said.
The murdered man’s son Stephane Rajavi earlier told the ATS news agency the document was signed by Vaud examining magistrate Jacques Antenen on March 20 and sent to the Swiss Federal Justice Office for "worldwide circulation".
The warrant names Iran’s former intelligence and security minister Mr Fallahian, who it said "decided on and ordered the execution of Kazem Rajavi", Le Matin reported.
Swiss authorities at the time of the killing suspected Iranian diplomats who left the country quickly after Mr Rajavi’s death, but no arrest warrant has been issued until now.