The complaint was filed by Hafid Ouardiri, the former spokesman for the Geneva mosque who now heads a Muslim association aimed at promoting interfaith dialogue. He says that by enacting the ban against minaret construction, Switzerland violated the European human rights convention which guarantees freedom of religion and against discrimination.
Ouardiri says he is acting on behalf of all Swiss who feel the way he does.
"We are fighting altogether to protect human rights and to protect Switzerland against racism and Islamophobia, so we think we are doing good - first for the Swiss people and for Switzerland as a country," said Hafid Ouardiri. "We are trying to help her in the fight against extremists."
Swiss voted in favor of banning minaret construction in a referendum last month that drew widespread condemnation. Now, a group of Swiss intellectuals is reportedly considering pushing for a new referendum to overturn the ban. Swiss media also report that at least two complaints against the ban have been filed in Swiss federal court.
About 500 protesters also gathered outside Switzerland's parliament last weekend to protest the ban. But nationalist politicians in Switzerland and elsewhere have praised the measure.
Of 150 mosques or prayer rooms in Switzerland, only 4 have minarets, and only two more minarets are planned. None conduct the call to prayer. There are about 400,000 Muslims in a population of some 7.5 million people.