The decision, announced on Wednesday, comes nearly two months after two Muslim schoolboys refused to shake their female teacher's hand at a school in Therwil, near Basel, because they said physical contact with a woman who wasn't a family member went against their religion.
The incident caused outrage across Switzerland, not only because it was seen as sex discrimination but because their refusal was considered an affront to an intrinsic part of Swiss culture.
Shaking hands is a habit Swiss people are taught from an early age as a sign of respect.
After the furore, the two boys were given temporary dispensation from shaking any teacher's hand – rather than just their female teachers – while authorities discussed the matter.
But that dispensation has now been quashed, meaning the teenagers will have to shake hands with all their teachers, regardless of their sex, or face the consequences.
In a statement, the department of education, culture and sport in Basel-Country said: “The public interest with respect to equality between men and women and the integration of foreigners significantly outweighs the freedom of conscience (freedom of religion) of the students.”
Refusing to shake hands on religious grounds would be to involve others in a “religious act” and is therefore different from the wearing of a headscarf or refusing to take part in swimming lessons, it said.
“The social gesture of a handshake is important for the employability of the students later in their professional lives,” it added.
Elementary schools in Basel-Country have been informed of the decision by education director Monica Gschwind, it said.
From now on, if a pupil refuses to shake hands their parents or guardians could be fined up to 5,000 francs.
Disciplinary measures which must be “educational, useful, necessary and proportionate” could also be taken against the child, including an oral warning or a debate with parents.