The biggest area to be affected is Sykehouse and surrounding villages when the lights went out on 350 properties at 6am.
A spokesperson for the Northern Powergrid said there had been "a problem with one of our underground cables that supplies your area."
The power is due to be back on by 12.30pm.
The power is also out on 20 properties in Edenthorpe and 10 in Woodlands. The problem is due to be fixed by about noon in both areas.