The London Fire Brigade was called just after 5.30pm on Friday (January 9) to Arbour Square in Shadwell.
Firefighters from Shadwell, Bethnal Green, and Poplar fire stations were dispatched to the scene, and one man was rescued by crews wearing breathing apparatus.
The London Ambulance Service treated the man for smoke inhalation.
The fire destroyed part of the first floor in a three-storey mid terraced house.
Crews from Shadwell, Bethnal Green, and Poplar fire stations were dispatched to the scene.
The fire was under control by 6.21pm.
A London Fire Brigade spokesperson said: “Candles are one of the most common causes of fires in the home and you should be careful when using them.
“This is a timely reminder to never leave candles unattended and keep them away from anything that could catch fire such as curtains, furniture or clothes.
“We recommend swapping traditional candles for LED flameless ones as they are much safer, but if you do use real candles, follow our simple safety tips.
“Firefighters recommend that you have a look at our online Home Fire Safety Checker to make sure there are no hidden hazards in your home.
“The online tool will ask you a series of questions that will help us work out the level of risk in your home, or the home of someone you care for.
“It only takes a few minutes to get tailored advice to keep yourself and loved ones safe from fire.”
