In a released video, she noted that she was finding a cancer for her "huge shock" after "incredibly difficult several months".
But at the same time she said that "it feels well and becomes stronger every day."
It is unknown what type of cancer in the princess. The Kensington Palace is convinced that it is fully recovering.
In her statement, Kate explains that when she was performed on the abdominal cavity in January, cancer was not known. But the tests after surgery showed that it was cancer.
"That is why my medical team advised me to undergo a course of preventive chemical therapy, and now I am in the early stages of this treatment," the princess said.
Kate said she thinks of all those who have cancer: "For anyone who faced this disease, please do not lose faith or hope. You are not alone."
She noted that the recovery after surgery took some time, and her family is now a priority for her.
The princess added that they with her husband Prince William had time to explain everything to the children - George, Charlotte and Louis - and assure them that everything would be fine with her.
She said that now their family needed "a little time, space and solitude."
The Prince and Princess of the Wales are expected to come with the royal family to Church on Easter Sunday.
The princess will not return to fulfilling their official duties.
The palace also stated that Prince William was not at the memorial service at the end of February precisely because Catherine was found cancer.
The royal couple was faced with public speculation and social networks about its health after surgery. From Christmas, she did not attend any official events.
In her video, she told about family support: "What William is next to me is also a wonderful source of consolation and reassurance. Like love, support and kindness that so many of you show. It means both of us."
The Kensington Palace reported that the video with the princess had shot BBC Studios, the BBC production unit, on Wednesday, March 20.
The BBC News statement said: "Kensington Palace, together with other media, informed the BBC News about this statement this day."

Photo author, Getty Images
At the end of January, Kate had surgery on the abdominal cavity. She spent almost two weeks at a clinic near the Ridzhntsi Park in the center of London. And now he does not perform the duties of a senior member of the royal family.
Earlier in the Kensington Palace emphasized that the operation was not emergency but planned, and was successful.
Kate has not appeared in public for a long time. She has recently posted her photo with children. But it was noticed a number of manipulations.

Photo author, Getty Images Signature to Photo, King visited St. Mary Magdalen's Church in Sanderingma in February
After the news on the hospitalization of the Princess of Wales, the Buckingham Palace was reported that the operation will also have to be transferred to King Charles III.
In early February it became known that the king had a cancer. But this is not prostate cancer. Although it was found during a recent treatment that the monarch passed through the prostate adenoma.
The British King Charles III occasionally appears in public.