The 65-year-old writer, known for his popular Kurt Wallander detective novels, delivered the news in a short but moving article in Sweden's Göteborgs-Posten newspaper.
"My anxiety is very profound, although by and large, I can keep it under control," he wrote.
Manning described how he had learned of the cancer two weeks ago on a visit to his orthopaedic surgeon in Stockholm for what he had thought was a slipped disc.
"When I went back to Gothenburg the following day I did it with a serious diagnosis of cancer," he wrote. "I do not have any particular memories of the journey back to Gothenburg. Only a deep sense of gratitude that my wife Eva was with me."
Tests at Gothenburg's Sahlgrenska hospital a few days later revealed several tumours.
"It was serious," Mankell wrote. "I had a tumour in my neck and also a tumour in the left lung. In addition, there were suspicions that it had spread elsewhere in the body."
He said that the idea of writing a chronicle of his disease came quickly.
"At a very early stage I decided to try to write about this, because it is ultimately about the pain and suffering that afflicts so many people," he wrote.
"I have decided to write it just as it is, about the difficult battle it always is," he continued. "But I will write from the perspective of life, not death."
Gabriel Byström, the culture editor at Götebergs-Posten, who has commissioned the articles, said that it was natural for Mankell to choose to write about his illness for the newspaper.
"Henning Mankell has been writing for the culture section of GP for a couple of years now, and he lives in a suburb of Gothenberg," he said.
Mankell is famous in the English-speaking world for his detective novels featuring Kurt Wallander.
The novels have been made into a TV series in his own country and played by the actor Kenneth Branagh in a British television adaptation.
In his native Sweden, he is also known as a playwright and leftwing activist involved in the Free Gaza movement.
Wallander joins a growing list of internationally acclaimed authors to decide to describe their struggles with the illness.
John Diamond, the British journalist and first husband of cookery writer Nigella Lawson, wrote about his throat cancer for the Sunday Times in the late 1990s.
The writer and journalist Christopher Hitchens won an award for his articles about the illness in Vanity Fair magazine in 2010.