The previously undisclosed probe is targeting Rifaat al-Assad, the older brother of the late Syrian dictator Hafez al-Assad.
Rifaat al-Assad, who is separately implicated in French and Spanish corruption probes, was forced into exile in 1984 after a failed attempt to overthrow his brother.
But Swiss authorities are investigating alleged offences committed when Rifaat al-Assad commanded military units suspected of slaughtering thousands of civilians.
In a statement, the Swiss attorney general's office (OAG) said that following a criminal complaint it had opened a "war crimes" case against a Syrian national in December 2013 in connection alleged offences committed in Syria in the 1980s.
The complaint was filed by TRIAL International, a rights group that works with victims and pushes Switzerland to prosecute alleged international criminals.
TRIAL said that much of the evidence it had compiled against Assad relates to his role in suppressing a 1982 rebellion in the Syrian city of Hama, where thousands of people were estimated to have been killed.
TRIAL noted that Assad's occasional visits to Switzerland gave authorities the opportunity to arrest him, in accordance with the Swiss principle of universal jurisdiction for major international crimes.
"The case is at a stalemate, despite the significant amount of evidence at hand," TRIAL said in a statement.
"The sluggishness of the OAG goes against Switzerland's international commitments," the organisation's director Philip Grant added.
TRIAL spokeswoman Chloe Bitton told AFP that the decision to go public four years after the probe was opened was made by lawyers representing Assad's alleged victims, who were frustrated with the lack of progress.
The OAG said the "very complex" nature of the investigation meant the probe would take time.
According to Bitton, the attorney general's representatives held an "informal" meeting with Assad at a Geneva hotel during one of his trips to the Swiss city in September 2015.
French and Spanish authorities have separately been cooperating on an embezzlement case targeting Assad, whose assets have been estimated at several hundred million dollars.
France filed charges against him in June last year.