Princess Anne, 66, is understood to have had some tests at Aberdeen Royal Infirmary on Wednesday.
Buckingham Palace said the Queen's daughter had been suffering from a bad chest infection and had cancelled her engagements on the advice of doctors.
She has been staying at Balmoral, the Queen's Aberdeenshire residence.
Princess Anne joined the Queen and other members of the royal family at the Braemar Gathering at the weekend.
The event on Royal Deeside, near Balmoral, is seen as the biggest in the Highland Games calendar.
A scheduled visit by the princess to HMP Grampian in Peterhead was cancelled on Thursday.
The Princess Royal has cancelled her public engagements next week because she is "feeling unwell", Buckingham Palace has said.