Officers were called to the northern town of Würenlingen after gunshots were heard shortly after 11pm on Saturday night. Three bodies were reportedly found.
Upon arrival, “several” bodies were found lying outside a house, as well as inside the building. Ambulance workers have been unable to give a cause of death.
According to a police spokesman, speaking to local radio, the shooter is also thought to have been killed in the incident.
All of those killed were adults, and investigators are working to identify the victims – as well as a possible motive.
Würenlingen, which is northwest of Zurich, is home to a community of about 4,500 people.
A news conference is expected later on Sunday from police, who have not yet confirmed how many people are dead.