Cheanne Nielsen, a member of the far-right Danish People’s Party (DPP), will be investigated for alleged racism following the remarks at its annual conference.
In a speech to the party faithful the Copenhagen delegate questioned benefits hand-outs to recently arrived migrants and accused them of “making a mess” of the country.
Police in the Danish capital confirmed they were investigating the remarks after a member of the public complained that they breached the country’s race hate laws.
During her hate-filled rant, Ms Nielsen said: “Why should foreigners take care of themselves, now that they can require rent and pocket money from the state as soon as they come here?
“They make a mess, they cheat, they steal, they rape and they kill.”
The remarks were apparently greeted with applause from party delegates in the room, but have been met with dismay and disgust from across the political spectrum.
Denmark’s government has already taken a harder line on immigration in recent months following unprecedented numbers of new arrivals, rolling out restrictions to limit the number of people settling in the country.
One of the more controversial policies is forcing migrants to pay into the system in the form of taxes before they can claim benefits.