The power cut was first reported by residents in LS17 and LS28 at 9.53am.
Northern Powergrid warned that more than 100 homes and businesses in the area could be left without power until 4pm today.
Engineers are at the scene working on the problem.
The Northern Powergrid alert said: "We've had to switch off the power for safety purposes whilst our engineers work on the cables and equipment that serves your area.
"We appreciate your patience and understanding."