A user of the social network called for the school to be closed over its alleged association with US-based cleric Fethullah Gulen, the man accused by Turkish president Recep Tayyip Erdogan as being behind the coup that attempted to oust him last Friday night.
The school's headteacher – unnamed in the press over fears for the safety of his family in Turkey – was worried enough by the threats to call the police and inform education authorities, said news agencies on Thursday.
A German national who has lived in Switzerland for several years, the head presides over a school that has 35 pupils and five teachers of Turkish or Balkan origin.
“The threats that we received are linked to the international hunt for supporters of the imam Fethullah Gulen,” he told news agencies.
“They are exaggerated, because our establishment is Swiss, neutral, secular and follows the cantonal curriculum,” he added.
“Our only goal is to deliver quality teaching allowing these young people to integrate.”
He acknowledged that the school's founders were partly inspired by the teachings of Gulen, whose followers run schools all over the world.
More than 260 people were killed and many more injured in the coup led by members of Turkey's military last week.
President Erdogan was quick to place the blame on Gulan, a Turkish spiritual leader and proponent of moderate Islam who has lived in the US since fleeing Turkey in 1999.
Last year Turkey declared the Gulen movement a terrorist organization.
Gulen denies involvement in the coup and has denounced the arrests and sackings of thousands of suspected Gulenists ordered by Erdogan in the past week.
On Thursday the European Union issued a statement calling for Turkey to respect the law and human rights after Erdogan declared a state of emergency for three months to “cleanse the supporters of the Fetullah Gulen terrorist organization from state bureaucracy,” the BBC reported him as saying.
In a statement, the Swiss government condemned the coup and gave its support to the “legitimately and democratically elected” Turkish government.
But it also urged it to “show restraint” in dealing with those arrested and respect “human rights and the rule of law in accordance with Turkey's international commitments”, including guaranteeing the independence of the judicial system and rejecting the death penalty.
“It is Switzerland's position that compliance with human rights includes the rejection of the death penalty,” it said.
In a press conference in Bern on Friday the Turkish ambassador in Switzerland said it was possible that the Turkish government "would launch procedures against Gulenists in Switzerland", reported the Tages Anzeiger.