The blaze, at Hawkhill Close, was reported just before 6am. A car was alight within a ground floor car park. The child did not require hospital treatment.
In a separate incident a woman was treated for smoke inhalation following a kitchen fire at a house in Delta Drive in Musselburgh at 5.45pm yesterday.
The 30-year-old was checked over by paramedics at the scene but did not go to hospital.