Work will be undertaken on Sunday July 31 to replace coping stones from the southern parapet and reset stones on the northwest corner of County Bridge, in Barnard Castle, which were damaged when a lorry shed its load.
The road is expected to be closed to all traffic from 7am to 3pm, but may reopen sooner if the repairs are completed sooner.
A signed diversion route for vehicles will be in place via Startforth, the Cross Lanes to Rokerby Park junctions of the A66 and Egglestone Abbey Bridge.
Pedestrians will also have a signed diversion route via Thorngate Footbridge.
Durham County Council wishes to thank the public for their patience and apologise for any inconvenience during this essential work.