The closure will allow workers to realign the parapet walls with the bridge's newly installed defences, but will also be used to make improvements to the pedestrian walkway.
Work on the bridge is part of the final phase of the Environment Agency's scheme to protect 3,000 homes in the area, which were badly affected by flooding in June last year.
Traffic will be diverted during the works but the Environment Agency, who were pleased by the level of local community cooperation at earlier stages of the project, are keen to minimise any disruption.
Project Manager, Anthony Myatt, said: "This is the last phase of the Selby flood defence scheme and the last time we will have to call on the patience of local residents. We will do all we can to complete the work as quickly as possible, but disruption to traffic from the diversion is inevitable."