Western Power Distribution said it received reports from households in the SY1 postcode north of the town centre shortly after 11am on Sunday.
The company said that 61 properties were affected, and that the issue was a result of low voltage.
Western Power said the affected postcodes included SY1 3JQ, SY1 3JH, SY1 3JG and SY1 3JL.
It is hoped the issue will be resolved this afternoon.
Meanwhile nine properties in the Dawley area of Telford are also without power, with the issue hoped to be fixed by 6.30pm.