Fedw-llwyd bridge on the B4355 between Knighton and Beguildy was shut on Friday.
Powys council said engineers found problems with the structural integrity.
John Brunt, cabinet member for highways, said: "I appreciate the inconvenience this will cause for users of that route but my main priority is the safety of everyone who uses that bridge."
The council said emergency repair work would be carried out and the bridge would reopen as soon as possible.
A bridge in Powys has been closed over safety fears.