Damian Green said it would be "undesirable" for Parliament to try to pass such a law which would be at odds with the UK's "tolerant and mutually respectful society".
Fellow Tory MP Philip Hollobone introduced a private members' bill which would make it illegal for people to cover their faces in public.
More than two thirds of voters back a ban like that approved almost unanimously by French MPs last week, according to a recent opinion poll.
But Mr Green insisted such a move was "very unlikely" to be copied here.
"Telling people what they can and can't wear, if they're just walking down the street, is a rather un-British thing to do," he told the Sunday Telegraph.
"We're a tolerant and mutually respectful society."
There were occasions when it was important to be able to see someone's face, he said.
"But I think it's very unlikely and it would be undesirable for the British Parliament to try and pass a law dictating what people wore."
Unlike France, the UK was not "aggressively secular", he said, suggesting the proposed ban across the Channel was being brought in to make a point.
Earlier, Mr Hollobone declared that he would not meet with burka or niqab-clad women at his Kettering constituency surgeries unless they lift their veils.
"If she said 'no', I would take the view that she could see my face, I could not see hers, I am not able to satisfy myself she is who she says she is.
"I would invite her to communicate with me in a different way, probably in the form of a letter," he told the Independent.
Shadow justice secretary Jack Straw, who sparked controversy in 2006 when he revealed he asked constituents to lift their veils, said he was opposed to a ban.
"I was seeking to generate a debate within a framework of freedom," he said, saying around half agreed to his request and half refused.
Mr Hollobone previously described the burka as "offensive" and "against the British way of life".
His Face Coverings (Regulation) Bill stands little chance of making progress in the Commons however.
The French legislation, which is backed by President Nicolas Sarkozy, will pass to the upper house, or Senate, in September.
SIC: TIUK