Northern Powergrid has confirmed that 60 properties in YO13 postcodes are currently without power due to "an unexpected problem" with cables and equipment.
A small number of properties in YO12 postcodes are also being affected by the aftermath of Storm Ciara.
The outage was reported at 6.54am, power is expected to be restored by 12pm.
Brompton & Sawdon Community Primary School, Snainton School and Hertford Vale Primary School will remain closed today as a result of the power cut.
Anyone who spots any damaged cables or other equipment is urged not to approach the area and report it immediately by calling 105.