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 weeknights until Tuesday 1 December, weather dependent.
Highways England project manager Phil Leng said:
We need to carry out emergency repairs to the bridge joints on Leven Valley Viaduct Bridge starting tonight as a precautionary measure. This work will be carried out overnight when traffic levels are at their lowest.
We apologise for the short notice of the closure but this work is necessary so the A19 can remain open and safe for drivers.
Clearly signed diversions will be in place via the A67, the A1044 Low Lane, Thornaby Road, the A174 Parkway to rejoin the A19.
Members of the public should contact the Highways England customer contact centre on 0300 123 5000.
Journalists should contact the Highways England press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.