Regional educational authorities issued the ruling in response to an earlier decision to exempt Muslim students from being obligated to shake their teacher's hand.
"A teacher has the right to demand a handshake," said a statement released on Wednesday by Swiss education authorities. As punishment for refusing to do so, parents or guardians of the students could face a fine of up to 5,000 Swiss francs ($5,000, 4,500 euros).
The decision followed a national controversy that erupted last month after two Muslim students in Basel-Country refused to shake their female teacher's hand, arguing that their faith forbade them from making physical contact with most members of the opposite sex.
In response, the school decided to exempt the Muslim students from shaking hands with any teacher. The decision drew fierce backlash from around the country, where shaking hands with teachers is a deeply entrenched cultural practice.
The Islamic Central Council of Switzerland (ICCS) said Basel-Country had exceeded its authority by overturning the school's decision and vowed a court battle. The group said mandating physical contact between individuals amounts to "totalitarianism."
The school said it was "relieved" at Wednesday's ruling and having "clarity on how to proceed."
Switzerland has an estimated 350,000 Muslim citizens, about 4 percent of its population.