Hinton Hall Bridge near Pontesbury will be closed for repair from Monday 28 October to Tuesday 5 November.
The repair work will involve taking down and rebuilding a section of damaged upstream parapet.
The bridge carries Hinton Lane over the Rea Brook to the south of Hinton near Pontesbury. The bridge must be closed to traffic while repairs are being undertaken, as the road is too narrow for the work to be carried out safely with the bridge open to traffic.
During the road closure, traffic will be diverted via the A488 and Hinton Lane.
Access for pedestrians and dismounted cyclists will remain available at the bridge throughout the works.
Steve Davenport, Shropshire Council’s Cabinet member for highways and transport, said: "It is appreciated that the bridge closure will cause some inconvenience, and everyone involved will do all that they reasonably can to reopen it as soon as possible.”