Amnesty International said a ban would set a "dangerous precedent".
In a statement, the human rights group said it would "violate the rights to freedom of expression and religion of those women who wear the burqa or niqab as an expression of their identity and beliefs".
The ban would be imposed in all buildings or grounds that are "meant for public use or to provide services", including streets, parks and sports grounds.
Exceptions could be made for certain festivals.
Those who break the law could face a fine of 15-25 euros (£13-£27) or a seven-day jail sentence.
The word hijab comes from the Arabic for veil and is used to describe the headscarves worn by Muslim women. These scarves come in myriad styles and colours. The type most commonly worn in the West is a square scarf that covers the head and neck but leaves the face clear.
The niqab is a veil for the face that leaves the area around the eyes clear. However, it may be worn with a separate eye veil. It is worn with an accompanying headscarf.
The burka is the most concealing of all Islamic veils. It covers the entire face and body, leaving just a mesh screen to see through.
The al-amira is a two-piece veil. It consists of a close fitting cap, usually made from cotton or polyester, and an accompanying tube-like scarf.
The shayla is a long, rectangular scarf popular in the Gulf region. It is wrapped around the head and tucked or pinned in place at the shoulders.
The khimar is a long, cape-like veil that hangs down to just above the waist. It covers the hair, neck and shoulders completely, but leaves the face clear.
The chador, worn by many Iranian women when outside the house, is a full-body cloak. It is often accompanied by a smaller headscarf underneath.
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