The inspection is needed to check for damage following an overweight vehicle crossing the bridge over the weekend.
Initial inspections have been carried out on the bridge but a more thorough assessment is now needed to see if any structural damage has been caused.
The work will be carried out on the Calverley Street bridge, with the Inner Ring Road (A58M) being closed in both directions from Wellington Street to Marsh Lane from 9pm until 5am on Thursday.
The closure will be fully signed with diversions in place, says Leeds Council.
A spokesman added: "All efforts will be made to minimise disruption while the work is carried out, which is required on safety grounds. Leeds City Council is looking into the cause of the issue."