The fire broke out in a tobacconist on the ground floor of the house at around 12.30am. Within two hours, all four floors were alight.
Some 40 people are registered as living in the building and the neighbouring house. Both buildings were successfully evacuated. Nobody was seriously hurt, although a few people suffered from the effects of smoke inhalation.
The fire was still burning six hours after the alarm was raised, but the fire was by then under control.
Four local fire brigades, including one from across the nearby border with Norway, were called to fight the blaze.
The building was said to have been destroyed by the fire.
“It’s sad that such a beautiful old building in central Strömstad has been destroyed,” said Strömstad Council’s head of communications, Peter Birgersson, to news agency TT.