David Lisnard said they are a "symbol of Islamic extremism" and might spark scuffles, as France is the target of Islamist attacks.
France is on high alert following a series of incidents including July's truck attackin nearby Nice.
Anyone caught flouting the new rule could face a fine of €38 (£33).
They will first be asked to change into another swimming costume or leave the beach.
This is not the first time that women's clothing has been restricted in France. In 2011 it became the first country in Europe to ban the full-face Islamic veil, known as the burka as well as the partial face covering, the niqab.