Lily Hartley was in Bradford Royal Infirmary when two rings, which had belonged to her late husband, were taken.
Her granddaughter, Emma Hartley, reported the theft on Facebook and said the rings had sentimental value.
Bradford Teaching Hospitals NHS Foundation Trust said it "sincerely apologised" to the family.
A spokesperson added they were "fully investigating the matter."
Read more about this and other stories from across West Yorkshire
West Yorkshire Police said it had been alerted to the theft relating to Mrs Hartley and also a second one at the hospital.
Officers said it believed two victims, both women in their 80s, had items of jewellery taken between the 26 and 29 March.

Peter Barnett, 44, travelled from Haddenham and Thame Parkway to London Marylebone, but dodged the full fare by claiming his journey began at Wembley in north-west London.
Chiltern Railways had argued he should pay back nearly £20,000 but the defence said the true value was £6,000.
Barnett, from Oxford, admitted fraud by false representation.
Deputy District Judge Olalekan Omotosho said: "There is a need not just to punish you for the offences but also deter others from committing offences."
She added: "It remains unclear why you acted so badly.
"You let yourself down and your family down, particularly in light of your profession as a lawyer."
Barnett admitted six counts of fraud by false representation between April 2012 and November 2014 and was ordered to pay back nearly £6,000.
City of London Magistrates' Court heard that Barnett - an Oxford graduate and former Rhodes scholar who also worked in the financial services sector - failed to pay for journeys on Chiltern Railways on 655 days between April 2012 and November 2014.
He was thought to have simply "tapped out" with an Oyster card, automatically being charged the maximum Transport for London fare.
Prosecutors had argued he should pay back £19,689, the full value of the cost of daily returns for the trips he made.
However, the defence claimed the value was a penalty imposed by the railway company rather than the true value, because if Barnett had bought a ticket it would have been a weekly one - rather than paying a daily fare.
The court heard that Barnett ran off when a member of station staff became suspicious about his story and called a supervisor, but had a change of heart and later handed himself in.
During an interview with British Transport Police, he confessed that he had been carrying out the scam since April 2012.
Barnett was also ordered to carry out 200 hours of unpaid work and be supervised for 12 months.
Hospital bosses have apologised after a woman in her 80s had jewellery stolen whilst in hospital.
[NEXT_CONCEPT]
A barrister who commuted by train for two years without paying has been given a suspended 16-week prison sentence.