Seven properties in Halesowen were affected by the power outage, said Western Power Distribution [WPD].
The area of disruption was situated around the Asda superstore near to the Cornbow Shopping Centre, in Queensway.
WPD said seven properties were "off supply" but that affected postcodes were B63 3AA, B63 3AU, B63 3AX and B63 4AJ.
A spokesman for WPD said: "We are aware of this power cut incident which was raised at 4.58am this morning [Thursday] and our engineers are working to get the power returned as quickly as possible.
"We are sorry for any inconvenience this is causing you."