The incident, in which the protester appeared to be crying, was captured by a Reuters photographer on Aug. 1 when a countrywide ban on the wearing of face veils in public took effect.
"The photo has made the police an involuntary actor in a very sensitive political debate which they should not participate in," said Marcus Knuth, a lawmaker with the anti-immigrant Liberal Party, which is the biggest in the government.
He and others alerted the independent complaints body over the gesture. "The police's job is to enact the law, not to hug people who are against it," he said.
The officer's lawyer, Torben Koch, said the officer felt she had handled the situation appropriately within her role as a "dialogue officer", a role specifically created to ease tension during protests.
"It is complete nonsense. As my client said, if it had been any other person in the same situation she would have done the same, so it has nothing to do with her wearing the niqab," Koch said.
The ban has exposed deep divisions in Danish society, with some arguing it upholds secular and democratic values and others that it infringes on freedoms of religion and self-expression.
Elsewhere in Europe, France, Belgium, the Netherlands, Bulgaria and the German state of Bavaria have all imposed some restrictions on full-face veils in public places.
The officer who embraced her, whose name has not been made public, is white and Danish.
Copenhagen police did not immediately respond to a Reuters request for comment.
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