NHS Ayrshire and Arran suffered a power cut at University Hospital Crosshouse in the early hours of Sunday morning.
The hospital went into emergency response, and the health board worked with local health and social care partnerships, the Scottish Ambulance Service, NHS 24 and NHS Lanarkshire overnight to minimise disruption.
Power was restored with no risk to patient safety, NHS Ayrshire and Arran said.
But the health board later announced that due to interruption to administrative systems, all outpatient appointments on Monday would be cancelled.
This includes clinics at University Hospitals Ayr and Crosshouse, East Ayrshire Community Hospital, Ayrshire Central Hospital and musculoskeletal appointments at Biggart Hospital.
Medical director Dr Crawford McGuffie warned there may be further disruption in coming days.
Patients have been asked not to attend appointments on Monday and to wait to be contacted for rescheduling. Those with concerns can call 01563 827070 for more information.
It is understood X-ray, chemotherapy and maternity services will go ahead in some cases.
Dr McGuffie said: “This has been an unavoidable decision and we understand that this will have an impact on a number of people who access our services.
"Unfortunately the administrative systems we rely on to run our outpatient clinics smoothly have not been fully restored at this point, so we will not be in a position to run these services on Monday.
“Our teams are working very hard to get all these systems operating normally and we hope everything can be resolved as quickly as possible. We are very sorry for the impact these appointment cancellations will undoubtedly have on our patients and want to apologise for any disruption caused.”
He added: “We are continuously appraising the impact of these administrative systems issues, which are unfortunately affecting many of our health and social care services and may lead to disruption across acute and community services more widely in the coming days.
"We will make further assessments early in the week and provide additional information for our citizens as soon as we have details on any further anticipated disruption.
“I would like to thank the public for their support at this time.”