Police said they were held not because of their veils but for joining an unauthorised protest against the ban.
France is the first country in Europe to publicly ban a form of dress some Muslims regard as a religious duty.
Anyone caught breaking the law will be liable to a fine of 150 euros (£133; $217) and a citizenship course.
People forcing women to wear the veil face a much larger fine and a prison sentence of up to two years.
Under the law, any woman – French or foreign – walking on the street or in a park in France and wearing a face-concealing veil such as the niqab or burka can be stopped by police and given a fine.
