Her statement may go some way to answering the rumours and wild speculation on social media that have arisen in recent weeks about the health of the princess, who has been absent from public royal life since Christmas Day.
The photograph, taken by her husband, heir to the throne Prince William, showed Kate, 42, smiling and looking well, surrounded by Princes George and Louis and Princess Charlotte.
"Thank you for your kind wishes and continued support over the last two months," Kate wrote in a message on X. "Wishing everyone a Happy Mother's Day."
Mother's Day is celebrated on Sunday in Britain. The photograph was taken earlier this week in Windsor where the family live, her Kensington Palace office said.
Kate spent two weeks in hospital in January after having surgery for a non-cancerous but unspecified condition. She has not been seen in public since and Kensington Palace has said she is unlikely to return to official duties until after Easter, which falls at the end of this month.
Britain's royals usually do not disclose details of illnesses, regarding all medical issues as private. But the long absence of the princess - normally a frequent smiling presence at charity and other events - has spurred speculation about her health.
Her office released a statement earlier this month, reiterating that it would be providing only "significant updates" about her recovery.
KING CHARLES' HEALTH
Kate's surgery came on the same day that palace officials said King Charles, 75, would also be entering hospital for treatment for an enlarged prostate.
During the king's hospital stay, his medical team discovered he had an unspecified form of cancer. The monarch has had to postpone his public engagements while he undergoes treatment although he has been pictured carrying out some of his duties as head of state.
Buckingham Palace also marked Mother's Day, posting a picture of Charles kissing the hand of his late mother Queen Elizabeth, who died aged 96 in September 2022.
"Wishing all Mothers, and those who are missing their Mums today, a peaceful Mothering Sunday," the accompanying message said.
