Police and fire crews are investigating the cause of the blaze, which happened in Croft Place in Larkhall, at around 6am yesterday.
At around the same time, firefighters dealt with a tenement fire in High Street, Johnstone, in Renfrewshire.
A team fought their way through the smoke to find discarded material had been set alight. One female resident was led to safety and was suffering from slight smoke inhalation.
A police officer who assisted at the scene was taken to hospital as a precaution.
A Strathclyde Fire & Rescue spokesman said: "These incidents, which struck in the early hours of the morning, shows how fire can strike anywhere at any time. Strathclyde Fire & Rescue is urging the public to join the fight against fire and help it prevent tragedy over the festive period."
He said the Johnstone incident highlighted the importance of ensuring combustible material is never stored or left in communal stairways of tenements and flats.
Chief Officer Brian Sweeney warned people to take extra care, adding: "The festive season always sees a marked rise in incident numbers, with increased risks from the lethal combination of alcohol, cooking and cigarettes."