The request follows a report in The Daily Mirror that said at least one attempt was made to access the private information at The London Clinic, a private hospital.
Catherine, who is widely known as Kate and whose husband Prince William is heir to the throne, spent two weeks there in January.
Details of her condition have not been released but her Kensington Palace office previously said it was not cancer-related and that the princess wished her personal medical information to remain private.
Health Minister Maria Caulfield said the rules on accessing patient information were “very, very clear”.
Patients’ Notes
“Unless you’re looking after that patient, or unless they’ve given you their consent, you should not be looking at patients’ notes,” she told LBC radio.
“My understanding is that police have been asked to look at it,” she said.
A statement from London’s Metropolitan Police said it was “not aware of any referral… at this time”.
We can confirm that we have received a breach report and are assessing the information provided,” a spokesperson for the Information Commissioner’s Office (ICO) said late on Tuesday.
The chief executive of The London Clinic added that “all appropriate investigatory, regulatory and disciplinary steps will be taken” over the alleged data breaches.
Catherine was at the centre of controversy last week after she admitted editing an official portrait of her and her three children that Buckingham Palace released on Mothering Sunday.
It further stoked online speculation about her health and whereabouts after she had not been seen at a public event since a Christmas Day church service.
In January, The palace said that she would require a lengthy recuperation and would not return to royal duties until at least April.
But instead of calming fears over her health, the edited picture sent the rumor mill into overdrive as the media scrambled to pull the picture.
Catherine apologized but faced criticism even from usually supportive media.
British media have said that Catherine is still not due to return to public duties until mid-April.