Two of the women covered their heads so completely only their eyes could be seen, while the third wore a headscarf but left her face showing, The Daily Mail reported. They spent a day with four Muslim women.
Much of the day, the women traveled around Sheffield, going into shops and other public places. The Muslim women also got a look at the inside a police station and the life of a policewoman.
Critics called the exercise a waste of time and money.
"This is a complete waste of police time and taxpayers' money," said Douglas Murray of the Center for Social Cohesion. "It's not the duty of police to empathize with particular sections of the community. It is the duty of the police to prevent crime and catch criminals."
A spokesman for South Yorkshire Police said the exercise is one of many to help officers learn about different sections of their community, although he said other exercises did not involve changes of clothing.