Addenbrooke's Hospital says it is currently experiencing significant issues with its computer network.
People are being asked not to go to A&E unless absolutely necessary and ambulances are being diverted to other hospitals.
The Cambridge University Hospital's Trust says emergency surgery is continuing but elective operations have been cancelled.
Outpatients should assume that appointments are going ahead unless they hear from the the hospital.
In a statement the trust says technical experts are working to resolve the problem as soon as possible and staff are working to a well-versed business continuity plan.