Police have fined a woman in a shopping centre car park outside Paris for wearing a niqab, or full-face Islamic veil, in the first enforcement of France's burqa ban.

The 28-year-old woman was stopped by police in the car park in Les Mureaux, north-west of Paris, at 5.30pm on Monday, the day the niqab ban came into force. Police said she was stopped "without incident" for a few minutes and given a €150 (£132) fine. She has one month to pay.

Under the law backed by Nicolas Sarkozy, it is illegal for women in full-face veils to go anywhere in public, including walk down the street, enter shops, use public transport, attend doctors' surgeries or town halls. They face a fine or a citizenship class.

On Tuesday morning another woman in a full-face veil was stopped by police after she tried to enter a town hall in Saint-Denis, north of Paris. Followed by a French TV crew, she had brought some paperwork to the town hall for a bureaucratic issue just before 11am. She was refused by officials on the grounds that she was wearing a niqab. On the way out police asked her to remove her face-veil to check her identity.

When she refused she was taken to a local police station, where she lifted her veil but insisted on putting it back on again. She was not fined but Le Parisien reported that she had been given a written reminder and a leaflet explaining that full-face veils were no longer allowed in public and she risked a fine.

After police warned that the law banning niqabs was "infinitely difficult" to enforce and would not be a priority, the interior minister Claude Guéant insisted the law would be fully applied in the name of "secularism" and gender equality.

The law comes at a moment of tension in France, where Sarkozy, at record low poll ratings before next year's presidential election, has been accused of stigmatising Muslims to win over the far-right vote and counter the rise of the Front National.

France's national consultative commission on human rights has reported a rise in attacks on mosques in 2010, warning that the political debate on niqabs, minarets and national identity had allowed a rise in "anti-Muslim feeling" on a certain "fringe" of French society.