Richmond Bridge, also known as Green Bridge, will close during the day next week for vegetation to be removed.
The work on the bridge at the bottom of Slee Gill is due to start on Monday, October 30 and be completed by Friday, November 3.
During the works, officials say a road closure will be required daily between 9.30am and 3.30pm.
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A diversion route via Catterick Garrison will be in operation.
Richmond mayor Stuart Parsons said they had been asking for the work to be done for two and a half years.
He added: “There are trees growing out of it and if they don’t do something it will collapse into the Swale.
“While it will be inconvenient for a week it’s better than it becoming structurally unsound and having to close for months.”
Pedestrian access will be maintained throughout the works period, officials say.