Saad, 32, one of Denmark's best-known dancehall performers, died in the accident early Sunday, said her mother, Kristine Saad.
She did not know the details of the accident, but said one of Saad's friends, Karen Mukupa, survived the crash.
Known by her first name, Natasja made her Danish breakthrough in 1990 when she formed the reggae band "No Name Requested" with Mukupa. Her first solo rap album was scheduled to be released in August.
Dozens of people, including Danish musicians, posted messages of condolences on Saad's home page Monday.
Danish tabloid B.T., citing Jamaican police, reported on its Web site that the accident happened on the outskirts the capital, Kingston, early Sunday.
Besides Mukupa and Saad, there were two men in the car, both of whom were in critical condition at a local hospital, B.T. reported. Mukupa was not seriously injured, the paper said.
"We should use shock therapy to sober up the Americans. In this case, the Americans will speak about the need to resume dialogue. There is no other option"
The United States is concerned about the current crisis in the relations with Russia and suggests returning to reasonable policies to avoid a nuclear war