"Unfortunately her medical advisers have said she must not travel," the foundation said in a brief statement.
The 10 million kronor (US$1.5 million; €1.1 million) prize will be presented to the 88-year-old author in London instead, it said.
The announcement said Lessing "had been ill for some time" without giving details. But foundation spokeswoman Annika Pontikis told The Associated Press that Lessing canceled the trip to Sweden because of her back.
"She has back problems. I don't have any further information on it, but she can't travel because of it," Pontikis said.
The Swedish Academy announced in October that Lessing had won the prestigious award, citing her "skepticism, fire and visionary power" in novels, short stories, memoirs and plays that reflected her own unexpected journeys across time, space and ideology.
She had been invited to collect the award at the ceremony in Stockholm along with the Nobel winners in chemistry, physics, medicine and economics on Dec. 10, the anniversary of the death of prize founder Alfred Nobel 1896.
The Nobel Peace Prize is presented in Oslo, Norway, on the same date.
"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