Details of the type of cancer have not been disclosed and aides would not say how long the course of treatment would last.
However, Kensington Palace said it is confident that Kate will make a full recovery.
In her heartfelt video statement, the future Queen revealed that she would have to take a break from royal duties to focus on her recovery. She also asked that the family "need some time, space and privacy" while she undergoes treatment.
Aides gave no indication of when Kate's return to royal duties could be but it is understood that there are no plans for the Prince and Princess of Wales and their family to attend the Easter Sunday church service next week.
It had been hoped that Kate would attend the annual Windsor service.
Last year the couple's youngest child Prince Louis made his debut at the private family event, alongside his siblings Prince George and Princess Charlotte.
However, the Wales family are focused firmly on safeguarding their children, with William set to take a break from royal duties over the holiday.
His children, who attend Lambrook School in Windsor, will have just under four weeks off, returning on Wednesday April 17.
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