The power cut has hit homes in the TF7 and TF8 postcodes of Telford, which includes Madeley, Ironbridge, Coalbrookdale and parts of Halesfield.
Western Power Distribution said that work on the issue could take several more hours.
"We are sorry about the ongoing power cut in Telford TF7 and TF8," they wrote.
"Our team is working on the issue and we now aim to restore supplies by 3pm."
Among those hit by the power failure is The Green Wood Cafe in Ironbridge. The business has had to close for the day because of the issue. They took to Twitter to let customers know.
"Sadly we have to close for the day as we're not expecting power back until just before we close," they wrote. "We'll be back tomorrow."