A man has been taken to hospital to be treated for the effects of breathing in smoke at the four-storey building on Turin Street, Bethnal Green.
Smoke was "pouring out of every window of the block" as flames engulfed the flat and spread to the roof, according to an eyewitness.
Bethnal Green Road has been closed as 72 firefighters tackle the blaze.
It is unclear how the fire started.
As the fire spread the roof of the building was reduced to "smouldering wood in about five minutes" according to eyewitness George Shankar.
"There was smoke everywhere, pouring out of every single window in the block of flats, and you couldn't see more than 50m down the road" Mr Shankar said.
Labour MP for Bethnal Green and Bow, Rushanara Ali, who is at the scene described residents as "anxious given what has happened in Grenfell tower".
But she said the scene was calm despite thick smoke being blown into the surrounding areas by high winds.
Residents have been evacuated after a fire broke out on the top floor of an east London block of flats.