The 33-year-old woman and her nine-year-old daughter escaped from their first floor home in Aberdeen's Clifton Road through a window and on to a ladder deployed by firefighters from the Grampian Fire and Rescue Service.
The pair were taken by ambulance to Aberdeen Royal Infirmary for treatment for smoke inhalation following the blaze.
Four fire engines from Grampian Fire and Rescue took around 20 minutes to bring the blaze under control.
Grampian Police and the fire and rescue service have launched a joint investigation into the cause of the outbreak.
A spokesman for Grampian Police said the fire was being treated as "suspicious".
He added: "The cause of the fire has yet to be established and anyone who has information regarding this fire is asked to contact Grampian Police or the charity Crimestoppers on 0800 555111."