CE Electric UK said about 400 customers in the Batemoor area of the city were without power.
A spokeswoman said there had been reports of damage to some appliances.
The power surge is thought to have been caused by thieves cutting a conductor at the substations as they stole copper from the sites.
The spokeswoman said engineers were working to restore power to the homes as quickly as possible
South Yorkshire Police confirmed it was investigating the thefts on Saturday morning.
A spokesman said they were working with the fire service and CE Electric UK.