Northern Powergrid said the LS1, LS17, LS2 and LS24 postcodes were affected after an unplanned power cut first reported at 10.14am.
-> Did you lose your phone at Leeds Festival? West Yorkshire Police may have itSeveral shops in and around the Corn Exchange in Leeds city centre have said they are without power.
They include Ground Up Coffee and Company, in the Corn Exchange, support service The Market Place, in New Market Street, and The Duncan Pub.
Ground Up and The Market Place have been forced to close for the day as they have no electricity or running water.
A worker in the area said the fire service were focused on the Out Of This World organic food shop in New Market Street.
All surrounding businesses are closed while the fire service deal with the situation.
-> Violent former soldier put noose around girlfriend's neck and tried to hang her in attack caught on cameraNorthern Powergrid said power was not likely to be restored until 6pm.
A statement on their website read: "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."
A West Yorkshire Fire and Rescue Service spokeswoman said they were called to New Market Street at 9.55am.
Two crews from Leeds Fire Station attended and all fire service personnel had left the scene by 11.30am.