The women were arrested along with several other people protesting in front of Notre Dame cathedral in Paris against the new law.
Jourrnalists at the scene said the arrests came after police moved in to break up the protest which had not been authorised.
On Saturday police arrested 59 people, including 19 veiled women, who turned up for a banned protest in Paris against the draconian new law, the first of its kind to be enforced in Europe.
Earlier, French police said they will be enforcing the country’s new burka ban "extremely cautiously" because of fears of provoking violence.
They fear Muslims extremists will use the law to provoke fights with officers, while rich visitors from countries like Saudi Arabia will also cause trouble .
All garments which cover the face were officially banned from first thing this morning, with offenders facing fines of 150 euros (£133).
But police admitted that they feared being accused of discrimination against Muslims, whether approaching women in tinderbox housing projects or on the Champs Elysee.
"The law will be very difficult to apply on certain estates," said Patrice Ribeiro, of the Synergie police union.
Referring to two Paris suburbs where riots regularly break out because of alleged discrimination against Muslims, Mr Ribeiro said: "I can’t see police going to book dozens of veiled women doing their shopping in Venissieux or in Trappes.
"It will be the same when a police officer is about to arrest a veiled Saudi who is about to go into Louis Vuitton on the Champs Elysees. In all cases, the forces of order will have to be measured and cautious in their behaviour."
Synergie has already instructed its members to view the ban as a "low priority", and Mr Ribeiro said there would "inevitably be incidents".
Mohamed Douhane, another Paris police officer and Synergie member, said he and his colleagues also "expected provocation by a minority."
Mr Douhane added: "Fundamentalist movements are eager to raise the stakes. The police know they will be held responsible for any public order disturbances."
Police have already been warned not to arrest women "in or around" mosques, and "citizen’s de-veilings" are also banned.
The strict instructions, from Interior Minister Claude Guent, are contained in a nine page circular issued to officers.
With tensions running high within the country’s six million strong Muslim community, officers have been told to look out for members of the public taking the law into their own hands.
Instead they will have to call the police, who will in turn have four hours to consider whether an offender should be fined.
This will apply to all garments which cover the eyes, although scarfs, hats, and sunglasses are excluded.
As well as a mosque, Muslims will also be able to put on a veil in the privacy of their own homes, a hotel room, or even a car, as long as they are not driving.
Police have already complained that they will have to waste time on "burka-chasing", with Denis Jacob, of the Alliance police union, adding: "We have more important matters to be dealing with."
The ban means France is officially the second country in Europe, after Belgium, to introduce a full ban on a garment which immigration minister Eric Besson has called a "walking coffin".
While French women face the fines and ‘civic duty’ guidance if they break the law, men who force their wives or daughters to wear burkas will face up to a year in prison, and fines of up to 25,000 pounds.
Posters have already gone up in town halls across France reading: "The Republic lives with its face uncovered."
Belgium introduced a full ban last year, although it has not been enforced with any vigour. A ban also looks likely in Holland, Spain and Switzerland.
There are no plans to introduce a similar ban in Britain, although politicians from the UK Independence Party and some Tory backbenchers have suggested one.
The Telegraph
