She is married to the Queen's paternal cousin Prince Michael of Kent, 78.
The concern for her health emerged after she had both of her Oxford/AstraZeneca jabs earlier this year, a source close to the princess told The Sun on Sunday.
The source added: "The princess has been unwell and has sought medical attention.
"It has been a worrying time for those around her.
"It has been difficult for those close to her to see her suffering. She's really been through it."