Reflections from the 37-storey building are claimed to have melted parts of nearby parked cars, blistered paintwork and caused tiles to fall.
Developers Land Securities and Canary Wharf said the scaffold screen would be erected at street level.
They told the BBC: “This solution should minimise the impact on the local area over the next two to three weeks, after which time the phenomenon is expected to have disappeared.”
Ali Akay, of nearby Re Style barber’s, said the position of the sun at a certain time of the day caused a ray of reflected light to start a small fire and burn a hole in his company doormat.
He said: “We were working and just saw the smoke coming out of the carpet. We tried to cut the fire down, there were customers in at the time and they were obviously not happy.”