Former minister for food and the environment Eva Kjer Hansen confirmed to Ritzau on Wednesday that she would vote against the proposal, which was announced by justice minister Søren Pape Poulsen on Tuesday.
That comes despite the Liberal party's parliamentary group leader Søren Gade saying that MPs would not be given free reign to vote how they pleased over the issue.
Hansen has previously spoken out against a proposed ban on the religious garment, calling it "out of proportion".
Meanwhile, the libertarian Liberal Alliance party, a member of the three-party coalition, has said that it would allow its members to vote as they saw fit over the proposal.
Earlier this week, the government formally proposed a ban on Islamic full-face veils such as the niqab and burqa in public spaces, making it likely to become the next European country to restrict the wearing of the religious garment.
"It is incompatible with the values in Danish society and disrespectful to the community to keep one's face hidden when meeting each other in public spaces," justice minister Søren Pape Poulsen said in a statement.
A violation of the ban would lead to a fine of 1,000 kroner (134 euros), with repeated violations fined up to 10,000 kroner according to the proposal.
Custodial sentences were also considered as a potential punishment, but this idea was later scrapped in a concession to the Liberal party, Ritzau reports.
The proposed ban says the "burqa, niqab and balaclavas where only eyes and mouth are visible are examples of clothes that hide the face".
But covering the face in a recognisable manner, such as wearing winter clothing, sports gear and masks for festivities, is exempted, in an apparent change from a draft version of the proposal reported last month.
"I expect that, even for those [Liberal MPs] it pains, this proposal by the government can be supported. That is why we are in government," Gade said.
But Hansen was critical of the proposal when an earlier draft of it was reported last month.
"By intervening with legislation against items of clothing, we are going too far in relation to the fundamental values of Danish society. It should be up to us to decide how to dress," she said at the time.
The former minister added that she remained "very much against the burka".
Should Hansen and Liberal Alliance MPs vote against the proposal, it would need votes from the opposition to gain the majority needed to pass through parliament.
That could potentially leave the Social Democrats with the deciding vote. The party, which is the largest in opposition, is said to be weighing its options over the proposal.
All other parties on Denmark's left wing are against the ban.
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