The man was taken to hospital by ambulance as firefighters tackled the blaze that ripped through the building in Leythe Road.
At least six other people are believed to have left the property before the arrival of the fire brigade on Tuesday (October 31).
Four fire engines and 21 firefighters and officers were sent to the scene just before 1pm, where part of a flat on the first floor of the building was alight.
Crews battled the flames for more than 90 minutes before the fire was brought under control.
A London Fire Brigade spokesman said: "Four fire engines and 21 firefighters and officers have been called to a fire at a block of flats in Leythe Road in Acton.
"Part of a flat on the first floor of the building is currently alight. Approximately six people left the building before the arrival of the Brigade."
The Brigade was called at 12.54pm and the fire brought under control at 2.27pm.
Fire crews from Acton, Chiswick, Hammersmith and Park Royal fire stations attended the scene.
Bus routes 440 and E3 were placed on diversion while emergency services dealt with the incident.
The cause of the fire is not known at this stage.
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