The bridge will shut for a period of 13 weeks, from Monday 3 July.
The bridge runs close to the ruins of Rievaulx Abbey and was constructed after a medieval crossing was destroyed by a flood in 1754.
The Abbey was the first Cisterian monastery to be founded in the North of England. It was founded by a group of monks from Clairvaux Abbey in France during the 12th century. The ruins of the site are now managed by English Heritage.
During the works, a pedestrian footbridge will be installed to allow continued access. As well as the erection of advanced warning and diversion signs.
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The repairs include strengthening the load capacity of the bridge by constructing a concrete saddle across its three spans. This process requires the removal of the road surface and fill material which means it must be closed to traffic.
Furthermore, a section of stonework will be taken down and rebuilt using existing and new stone.
Commenting on the works, Executive member for highways and transport, Cllr Keane Duncan, said: "This is a very popular road due to its location near to Rievaulx Abbey.
"The repairs are essential to maintain the safety of the bridge for the use of residents, and visitors for many years to come.
"We would like to take this opportunity to apologise in advance for any disruption that this may cause."
Commenting on the potential disruption, Cllr George Jabbour, who represents the Helmsley and Sinnington division on North Yorkshire Council, said: "I know that our officers have done everything possible to minimise potential disturbance, including the plans to install a pedestrian footbridge."
