There are currently only two minarets in Switzerland, one in Zurich and one in Geneva and the call to prayer is not made from either of them.
The campaign has to gather 100,000 signatures by November 2008 to force a national vote on the initiative which, if it gains a majority vote, would then be written into law.
Ulrich Schlueer, a Swiss People's party parliamentarian for Zurich who is heading the initiative, said: "We have no doubt that we'll reach the goal.
"We've now been collecting for a week and we've already got 10,000 signatures."
But Samuel Schmid, a cabinet minister for the party, has said he is against the initiative, warning it was taking his party colleagues down the "wrong road".
"We would not solve any problems with such a move," Schmid was quoted as saying in the Sonntags Zeitung newspaper.
Official statistics show there are an estimated 311,000 Muslims in Switzerland, which has a total population of 7.5 million people.
A ban on minarets on religious grounds would go against the Swiss constitution, which guarantees freedom of religion.