London Fire Brigade was alerted to the incident on Manwood Street in North Woolwich just before 1pm. Some 15 fire engines and 125 firefighters are tackling the blaze on the 17th floor of the building.
Firefighters are also working to extinguish a fire on grass opposite the tower block.
The cause of the blaze is not yet known.
Footage shows flames and thick plumes of smoke billowing from the building.
It comes a day after the UK recorded its hottest ever temperatures as the mercury soared past a sweltering 40C.
Firefighters faced their busiest day since the Second World War on Tuesday as blazes broke out across the country in the extreme heat.
In a statement, the London Fire Brigade said: “Fifteen fire engines and around 125 firefighters have been called to a flat fire on Manwood Street in North Woolwich.
“A flat on the 17th floor of the building is alight.
“Firefighters are also tackling around one hectare of grass opposite the block.
“The Brigade’s 999 Control Officers have taken more than 105 calls to the blaze.
“The Brigade was called at 12.49pm.
“Fire crews from Shadwell, Dowgate, Dockhead, Shoreditch and surrounding fire stations are at the scene.
“The cause of the fire is now known at this time.”
Newham Mayor Rokhsana Fiaz tweeted: “I’m with @NewhamLondon Chief Executive at the sight of a serious fire incident at Manwood Street in North Woolwich, near London City Airport.
“The Fire Brigade is aware of the incident and will be tackling the blaze.
“Our council resources will be made available as needed.”