The Duke, who is 77, was taken ill on Sunday night but staff in his private office went out of their way to make clear that his condition is "not serious" and he is expected to resume his royal duties in due course.
The fact that he has only cancelled engagements for the next three weeks will increase speculation that he suffered a so-called "mini stroke" or transient ischaemic attack (TIA), which is caused by a momentary lack of blood to the brain.
People who suffer from TIAs are typically told they must not drive for a month, a similar timeframe to the one the Duke has given himself to get back to work.
The Duke was taken to University College Hospital in London on Sunday night before being transferred to the King Edward VII Hospital, where the Queen was treated this month for symptoms of gastroenteritis.
Palace sources said his stroke was “mild” and he has been well enough to speak to royal household staff since he was admitted to hospital.