The work on the Grade II bridge across the River Wye at Bredwardine, which was built in 1769, will continue until Friday, June 9.
Repairs are required to the parapets on the bridge which are becoming dangerous.
Workmen will be on site between 9am and 5pm each weekday. During these hours the bridge will be closed to motorists, although pedestrians will still be able to cross.
"We're keeping disruption to a minimum by ensuring the bridge can be used by motorists before 9am and after 5pm," said Stephen Oates, Herefordshire Council's Head of Highways and Transportation.
"We considered allowing traffic to cross the bridge permanently during the works but the bridge is simply too narrow to allow our workmen to carry out the repairs in safety.
"We're aware that the Hay Festival takes place at the end of May. However, this bridge is not on a main route in and out of Hay, and there is no work on the two weekends of the festival so we expect any traffic disruption to be minimal," he added.
Herefordshire Council has liaised closely with the local Parish Council and is having to work within strict Environment Agency guidelines which dictate conditions such as what time of the year the work can take place and the environmental impact of scaffolding being erected in the river.
The work is likely to cost in the region of around
£20,000-£25,000.