Contractors for Highways England will be carrying out the work on the northbound carriageway between the A67 Thirsk Road and the A174 Parkway Interchange.
Work will take place between 8pm and 6am and is expected to be completed by Wednesday 23 March; this is dependent on the weather.
Highways England project manager Phil Leng said:
We need to carry out repairs to the bridge joints on Leven Valley Viaduct Bridge starting tonight. This work will be carried out overnight when traffic levels are at their lowest.
This is essential maintenance work that will ensure the bridge can be safely used by drivers for many years to come.
Clearly signed diversions will be in place via the A67, the A1044 Low Lane, Thornaby Road, the A174 Parkway to rejoin the A19.