Officials are looking into the Gasworks Pipe Bridge after a structural assessment raised safety concerns.
The bridge links the Isis towpath with Friars Wharf and St Ebbe's in Oxford city centre.
It has been temporarily closed due to concerns it could cave in if overloaded, or in strong winds.
The bridge is owned and maintained by Oxford City Council, but as highway authority, the county council is responsible for ensuring safe passage along the footpath.
A jointly funded structural assessment raised concerns about the safety of it and the city council is now urgently commissioning further technical work to understand the options.
There are two alternative nearby pedestrian routes across the river and diversion signs are being put in place.
A spokesperson for Oxfordshire County Council said: "The safety of the public is our paramount concern when it comes to these matters.
"There are alternative crossing facilities within a reasonable distance of the affected bridge, and diversionary routes will be in place for cyclists and pedestrians. We will continue to liaise and work with Oxford City Council to understand the best solution to repair or replace the structure."
Oxford City Council added: "The temporary closure of the bridge will undoubtedly cause some inconvenience for users, but the safety of the public must be the primary concern.
"We will now work swiftly with our partners at the County Council with the aim of examining options for the future of the bridge."