The closure will be in force between 1pm and 5pm today and diversion routes will be in place for high-sided vehicles.
The area around the base of Bridgewater Place can be gripped by a dangerous wind tunnel effect during stormy weather.
Pedestrian Edward Slaney, from Sowerby Bridge, near Halifax, was crushed to death by a truck that was blown off its wheels close to the building in 2011.
Work started earlier this year on a scheme that will see a system of wind-deflecting barriers and screens being put in place at the site.
The council has also installed a reinforced glass shield on the pavement at Great Wilson Street as an interim measure to help tackle the Bridgewater Place problems.