Buckingham Palace revealed on Monday that Charles, on the throne for less than 18 months since the death of his mother Queen Elizabeth, was suffering from a "form of cancer" and would postpone his public engagements to undergo treatment.
Charles' younger son Prince Harry, estranged from the royal family, is due to arrive in Britain shortly and his elder brother, heir-to-the-throne Prince William, is expected to step up to fulfil some of the monarch's duties.
Sunak said he had been "shocked and sad" at the news.
"All our thoughts are with him and his family. You know, thankfully, this has been caught early," he told BBC radio.
Charles is planning to continue with much of his private work as monarch including his weekly audience with the prime minister and dealing with state papers, and Sunak said he was in regular contact with the king.
"That will of course continue as normal and we'll crack on with everything," he said.
Charles spent the night at his Clarence House home near Buckingham Palace on Monday after beginning a series of out-patient treatments.
The cancer was discovered when Charles spent three nights in hospital last month where he underwent a corrective procedure for a benign enlarged prostate. Beyond confirming it is not prostate cancer, the palace has not given any further details.
SURPRISE DIAGNOSIS
The surprise diagnosis dominated Britain's newspapers on Tuesday. "Nation's shock as treatment starts" was one headline in tabloid newspaper The Sun.
It is the latest blow for Charles during his year and a half on the throne.
Early last year, Harry published his autobiography "Spare", which contained damning revelations about his father and elder brother, while Charles has also had to contend with ongoing allegations against his brother Prince Andrew relating to the late sex offender Jeffrey Epstein.
Harry, who quit royal duties in 2020, is flying back to Britain from California where he lives with his American wife Meghan and two children after Charles told him and his other immediate family of his diagnosis.
The king's cancer revelation comes as Kate, the Princess of Wales and wife of heir William, also recuperates at home after spending two weeks in hospital following planned abdominal surgery for an unspecified but non-cancerous condition.
She is not expected to return to public duties until after Easter and the absence of the senior figures will put pressure on the other working royals to perform extra engagements.
Charles has always been keen to have a more slimmed down monarchy but with his younger brother Andrew and Harry no longer involved, all those who currently carry out royal engagements are aged over 50 apart from William and Kate.
"After the upheavals caused by the death of the late Queen and the controversies surrounding the Dukes of Sussex and York (Harry and Andrew), the hopes after the Coronation were for a period of calm and consolidation," the Daily Telegraph said in an editorial.
"But illnesses cannot be predicted or avoided, not even by a man who has looked after himself so well. We, along with the rest of the nation, wish His Majesty a speedy recovery."
