The brothers, aged 14 and 15, had informed education officials in the northern municipality of Therwil that physical contact with women who are not family members violated their faith.
They were then exempted from a Swiss custom of pupils shaking teachers' hands, with Therwil officials instructing them to avoid contact with male teachers as well to avoid gender discrimination.
But the compromise sparked a heated response from leading Swiss politicians including Justice Minister Simonetta Sommaruga who insisted that "shaking hands is part of (Swiss) culture".
Basel-Country spokesman Adrian Baumgartner, in an email, confirmed a report from the ATS news agency on the suspension.
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The report also noted that such suspensions are common in citizenship procedures as authorities often require supplemental information about the families concerned.
Amid the media storm that surrounded the handshake exemption, Basel-Country requested an expert legal opinion, which Therwil pledged to follow.
The father of the two boys, an imam based in Basel and a Syrian national, moved to Switzerland in 2001 and was granted asylum.