There are around 100 firefighters battling the blaze on the scene and 20 fire engines.
Dramatic footage on social media captured the fire and the smoke billowing through the capital and debris falling from the building, which is opposite Aldgate East tube station.
The London Fire Bridgade tweeted: “We now have 15 fire engines and around 100 firefighters dealing with the fire on 17th floor of a block of flats on #Whitechapel High Street. One of our 64 metre ladders has also been sent to the scene.”
The Brigade’s 999 Control Officers have taken more than 50 calls to the blaze.
They were called to reports of a fire at 3.53pm.
London Fire Brigade said: “We’re dealing with this fire on #WhiteChapel High Street. Ten fire engines & 70 firefighters are at the scene. Please avoid the area if possible.”
Fire crews from Whitechapel, Shoreditch, Dowgate, Bethnal Green, Dockhead, Old Kent Road, Islington and surrounding fire stations are at the scene.
The cause of the fire is not known at this stage.
The Metropolitan Police said the building is being evacuated.
A spokesperson for the force said: “We were called to the scene at 1555 to reports of a fire on Whitechapel High Street by the emergency services.
“The building is being evacuated.”
Meanwhile, the London Ambulance Service is asking local residents to keep their windows closed and stay indoors.
Mayor of London Sadiq Khan said he was in contact with the Fire Commissioner and urged Londoners to avoid the area.
Rushanara Ali, Labour MP for Bethnal Green and Bow, tweeted: “I am extremely concerned about the fire in a high-rise building on Whitechapel High Street.
“I am extremely grateful for the efforts of all 100 firefighters at the scene. Please avoid the area as our firefighters seek to bring the fire under control.”