He has suffered for many years from ulcerative colitis, an inflammatory bowel disease, but his condition is thought to have worsened recently.
Public broadcaster NHK said the 65-year-old wanted to avoid causing problems for his government.
Last year, he became Japan's longest serving prime minister. His current period in office began in 2012.
It appears that he will not step down on Friday but continue to serve until a successor is selected by his ruling Liberal Democratic Party (LDP).
In 2007 he resigned abruptly from an earlier term as prime minister because of his struggles with ulcerative colitis, a chronic condition affecting the large intestine, that he has lived with since he was a teenager.
Mr Abe has a reputation as a staunch conservative and nationalist, and for stimulating growth with his aggressive economic policy known as "Abenomics".