The 71-year-old former Beatle had planned to hold concerts in Japan and South Korea as part of his world tour.
He was scheduled to perform at Jamsil Sports Complex Main Stadium in Seoul on May 28 in what would have been his first concert in South Korea.
His illness caused him to miss his four scheduled concerts in Japan, including two in Tokyo this past weekend.
Seoul-based Hyundai Card Co issued a statement citing Sir Paul as saying he is "sorry to be letting fans down", and that he hopes to visit South Korea soon.
The statement said Sir Paul was still not feeling better and the cancellation was unavoidable.
Yesterday the official site of Sir Paul's Out There Japan Tour 2014 said his doctors were ordering "complete rest".
He is also due to play 19 US performances later this year.