Firefighters were called to the building in High Bank, Haywards Heath, at around 5pm this afternoon (Thursday February 25).
The blaze broke out in a first floor flat in the three story building.
A spokesman for the fire service said crews rescued a child from the property.
They added the child suffered smoke inhalation and was taken to hospital by ambulance. No serious injuries were reported.
The fire is believed to have been caused by unattended cooking. It has now been extinguished.
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