Details of the 92-year-old's medical problems were not released, at the request of his family. CBS said the writer's condition was stable.
Rooney delivered his 1,097th and final essay on Oct. 2, saying it was a moment he dreaded.
The three-time Emmy-winner had a long career as a writer. He worked for the military newspaper Stars and Stripes and wrote four books about World War II. He wrote for entertainment personalities Arthur Godfrey and Garry Moore and had a longtime partnership with newsman Harry Reasoner.
The Associated Press contributed to this report.