A spokesman told LCN that the building is at the end of a row of three shops, and the fire started in one of the neighbouring rubbish bins during the early hours.
About a third of Johnson's roof was destroyed, but the part of the building where garments had been stored suffered the least damage and, because of the time, nobody was hurt.
Johnson set up a helpline for customers worried about their clothes.
In January this year Johnson set up a restoration drycleaning service based in Oldbury so garments were taken there, and most have been restored.
Although the roof will take some time to restore, the company hopes to have a temporary unit in place and operational very shortly.
A police statement said: "The blaze is being treated as suspicious."
