Staff at M&S on Market Street told the Express & Star that the power had been out since 4am, and remain unsure of when the shop would reopen.
Other businesses as well as the police station and courts were also affected by the power outage, while The Mander Centre has remained largely unaffected and remains open.
National Grid said properties with the postcodes WV1 3AA, WV1 3EY and WV1 3LQ are affected by the high voltage incident which was first reported at 4.18am.
It describes high voltage incidents as ones that "tend to be larger, affecting the wider area and could mean your neighbours are off supply too".
In a statement, the electricity provider said: "We are aware of this power cut incident which was raised at 4:18am this morning and our engineers are working to get the power returned as quickly as possible. We are sorry for any inconvenience this is causing you."
They later told the Express & Star: "There was a fault on our High Voltage network causing 62 customers to lose supply. Most customers were restored, but there are two customers remaining off supply. Generators are in transit and shall be connected to these two customers.
"We would like to apologise for any inconvenience caused."
Hearings at the Wolverhampton Combined Court in Pipers Row were being transferred to the magistrates court in North Street due to the issue.