The law came into effect on Wednesday.

The woman has been identified as a 28-year-old, who was fined after she got into a scuffle with a fellow woman who tried to take it off  her.

The said incident took place at a shopping centre in Horsholm, 25 kilometres north of Copenhagen, the national capital.

Ever since its introduction earlier this week, the new law has been criticised, with hundreds of women taking to the streets to protest the order.

According to the federal order, "anyone who wears a garment that hides the face in public will be punished with a fine" in Denmark.

Image: Screengrab from YouTube