The narrow-gauge tracks are still in place near the Millennium Bridge on the banks of the River Ouse but have been exposed by shifting silt in the aftermath the floods caused by Storm Ciara and Storm Dennis last month.
They form part of what was once a horsedrawn railway that led from the Ouse wharves to the army barracks in Fulford.
The tracks were just 18 inches apart and were used to deliver explosives and military supplies from Ordnance Wharf to the base.
The line ran parallel to Hospital Fields Road but much of it has now been covered over by new development.
The section visible today formed part of a siding.
The army depot, today known as Imphal Barracks, was built in the 1870s and Ordnance Wharf began operating in 1888.
At one time, the line had points and turntables.