Ferguson, 63, who was married to Prince Andrew, was given the diagnosis at a routine mammogram screening and underwent successful surgery, the representative said.
"She was advised she needed to undergo surgery which has taken place successfully," the spokesman said.
"The Duchess is receiving the best medical care and her doctors have told her that the prognosis is good."
She reportedly left the King Edward VII Hospital in Marylebone, central London - which has treated the royal family for decades, on Sunday and is said to be recovering with her family at Windsor.
Before going to hospital, she spoke about her diagnosis on her new podcast Tea Talks with the Duchess and Sarah, which is released on Monday.
It was reportedly recorded before her operation and had been due to air on Thursday, before being put off until after she was discharged.
"The duchess wants to express her immense gratitude to all the medical staff who have supported her in recent days," her spokesman said.
"She is also hugely thankful to the staff involved in the mammogram which identified her illness, which was otherwise symptom free, and believes her experience underlines the importance of regular screening."
The Sun reported that the Duke of York, 63, and their daughters Princess Beatrice, 34, and Princess Euegnie, 33, are by her side as she recovers.
The grandmother-of-three was not at Royal Ascot earlier this week as she was being treated in hospital.
The duchess is a patron of the Teenage Cancer Trust and spoke at a Breast Cancer Foundation gala in 2019.
Beatrice was spotted with friends at Glastonbury on Sunday, the final day of the festival, and was at Royal Ascot earlier this week.
with PA
29°C