According to Swiss media three cases of people in clown masks threatening others have occurred in the city over the past few days.
While two cases were relatively harmless, one was violent, with a masked clown punching the victim in the stomach, said the 20 Minuten paper after a report by a local radio station
As yet the perpetrators are unknown.
The incidents mean Switzerland is the latest country to succumb to the clowning craze, which has become a worldwide phenomenon after spreading from the US.
Sightings of people dressed as clowns and frightening children have since been reported in the UK and across Europe.
In Germany five incidents involving scary clowns were reported last week, including one in which a masked assailant hit a man with a baseball bat.
And in Sweden, where there have been a number of incidents, an eight-year-old boy leapt from a balcony to escape a man in a clown suit who turned up at the door of the family home.
Speaking on the radio, Zurich police spokesman Stefan Oberlin said it wasn’t only the violent clowns who could face charges.
“Wearing a mask and running after someone with the intention of scaring them is also a punishable act,” he said.