Sculcoates Bridge will close to pedestrians and cyclists from Monday 22 March.
The closure will come into effect so that emergency repairs can take place to the footpath after it was damaged by the use of motorcyclists.
The repairs will take two weeks before reopening to pedestrians and cyclists.
Daren Hale, portfolio holder for economic investment, regeneration and planning, said: “We know that this is a popular route for many pedestrians and cyclists, and we apologise that we are having to take the course of action.
“Unfortunately a small minority of people have been using this bridge illegally, by driving motorbikes and mopeds over it.
“This is a listed structure, so any work has to be carried out in keeping with the original features of the bridge.”
Plans for the long-term future of the city’s most historic bridge will include an extended refurbishment, after a decision was taken at a Hull City Council cabinet meeting last month.