The Co-operative Food branch on High Street is shut until further notice while a specialist company carries out drying work on an upstairs room which saw a water boiler overflow.
The branch houses Dawley's Post Office, with the next nearest offices in Malinslee, Aqueduct and Horsehay.
The incident caused damage to the electricity supply according to the TelfordLive Facebook page.
The site quoted a member of staff who said they were sorry for any convenience but it wasn't safe to turn the electricity back on and that the store would be shut until further notice.
A spokesman for Co-Op head office said they were aware of the situation and that it could take time for stores to reopen after suffering this type of damage.