Shropshire Council said the work would be to the Clun No. 2 Bridge.
A spokesman said: "Proposed bridge repair work starting on Friday, July 22, will require the temporary closure of Clun No 2 Bridge, which carries an unclassified road over a tributary of the river Clun, along Woodside Farm Junction to the Waterloo Lane end of Clun."
The closures will be limited to 9.30am to 4pm Monday to Friday.
The council said that the work would involve repairs to the downstream parapet and general re-pointing.
A diversion route will be signposted while pedestrians and dismounted cyclists will still be able to use the bridge throughout the work.