NHS Forth Valley said the break-in happened last month at the hospital's audiology department when the offices were closed.
The health authority said the laptop was kept in a locked cupboard and was password-protected.
It contained names, addresses and audiology details of the patients.
NHS Forth Valley said the laptop had yet to be recovered and that it was working closely with Central Scotland Police on the case.
The authority said the risk of the information being accessed by the thieves was "very low".
Patients whose details were on the laptop are being contacted to advise them of the situation and a helpline run by specialist staff to deal with particular queries has been set up.
Police have appealed for anyone with information about the theft to contact them.