Egemen Bagis reportedly made the comments to a journalist last week during a visit to Zurich, where he was at a concert by Turkish singer Sezen Aksu after attending the World Economic Forum's annual meeting in Davos.
"We have ordered a police inquiry," Andrej Gnehm from the Zurich prosecutor's office told the Swiss news agency, confirming a report in the NZZ am Sonntag newspaper.
According to Turkey's English-language newspaper Today's Zaman, the minister was asked about his views on a newly-adopted French bill criminalising denial of the Armenian genocide and he responded: "Switzerland is another country where it is a crime to deny the so-called genocide."
"Here I am in Switzerland today, and I'm saying the 1915 incidents did not amount to genocide. Let them come arrest me."
The paper said a complaint had been filed by members of Switzerland's Armenian community.
The facts of the case are not yet clear, Christine Braunschweig, who is in charge of the case, told ATS.
"We don't know at the moment exactly what was said."
Meanwhile, Turkey has summoned the Swiss ambassador in Ankara, Raimund Kunz, to the foreign ministry over the incident, Turkish news agency Anatolia said.
During the meeting, Turkish Secretary of State Feridun Sinirlioglu told the ambassador that the incident was "unacceptable," said the news agency, quoting diplomatic sources who spoke on condition of anonymity.
Several people have been charged in Switzerland for denying the Armenian genocide. Among them was Turkish nationalist Dogu Perincek, who brought the case to Switzerland's highest court where he lost his appeal.
Armenians say up to 1.5 million of their forebears were killed in 1915 and 1916 by the forces of Turkey's former Ottoman Empire.
Turkey disputes the figure, arguing that 500,000 died. It also denies this was genocide, ascribing the toll to fighting and starvation during World War I and accusing the Armenians of siding with Russian invaders.