Danish police are searching for unknown attackers who set fire to the immigration minister's car.
Rikke Hvilshoj, her husband and two young children were rescued from their house, which also caught fire as a result of the attack.
A group calling itself "Beatte Without Borders" has said it carried out the attack, condemning the government's "racist immigration policy".
The minister and other senior politicians have been assigned guards.
Threat
The attack took place at 0300 local time (0100 GMT). Mrs Hvilshoj, 34, was woken up by a "loud bang". When the rescuers arrived, parts of her house were in flames, too.
"I am shaken and angry," she said.
The group that said it carried out the attack sent a statement to various Danish media, which said: "We cannot watch passively, while the official Denmark carries out its racist immigration policy.
"That's why we are taking action now."
The group is unknown, but police have cordoned off the area around the minister's home in an effort to find clues that could lead to their capture.
Harsh punishment
The family has been moved to a secret address. Meanwhile, the minister herself and other of her senior colleagues in the government have been assigned bodyguards.
The attack has come as a shock to Denmark's open society where it is not unusual to see ministers and other public figures go shopping, cycle and live their everyday lives among the rest of the population.
Justice Minister Lene Espersen says that given the fact that there were children in the house, the attackers could get life imprisonment.
The Danish government, which was re-elected in February, has introduced some of Europe's toughest restrictions on immigration, leading to criticism from Europe's human rights watchdog, the Council of Europe.
Nevertheless, the centre-right government insists the measures are right and fair.
Immigration tension
The attack comes less than two weeks after a shooting in Norrebro, another part of Copenhagen, involving members of the immigrant community. A young man was killed by a nightclub bouncer, while another was wounded.
When a leading Muslim cleric, Abu Laban, suggested the hand-over of "blood money" from one family to another as a way to settle the dispute peacefully, the immigration minister rejected the idea as "medieval".
"Nor do we trade camels in Denmark", was Mrs Hvilshoj's response to the idea.
But reports say that the family of the doorman who fired the fatal shot has agreed to move out of Copenhagen as a way to compensate for the killing.
The agreement has been sharply criticised by experts in criminal law who say it is unlawful coercion and goes against the Danish sense of democracy.
Only the courts can resolve murder cases in Denmark.
So, while some Danes are asking the government to loosen the tough immigration restrictions, others fear that parts of those already in the country are developing into a parallel society where ancient traditions threaten Danish law.
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