Fire crews rushed to Hawthorn Street in Springburn after they received an emergency call around 7:20 am on Wednesday.
Although the burning property was empty, two men, two women and two children were led to safety from neighbouring flats.
One of the rescued children was treated for smoke inhalation before being taken to Yorkhill hospital in the west end, and the five others were checked at the scene.
Three vehicles from Springburn and Maryhill attended the blaze, which started when a discarded cigarette set fire to rubbish in a bin.
Station Manager John McKenna said: "Thankfully this incident did not cause a tragedy but, even where no-one is hurt, house fires can cause immense damage and the loss of cherished possessions.
"We need people to ensure cigarettes and other smoking materials are always properly put out."