James Corfield, 19, had not been seen since he left the White Horse pub in Builth Wells in the early hours of last Tuesday morning.
Dyfed-Powys Police confirmed a body was found in Builth Wells on Sunday afternoon.
A force statement said: "The body has not been formally identified at this time."
It added: "The family have been made aware of the development and are being supported by a family liaison officer."
Brecon Mountain Rescue Team wrote on social media the team involved in the search for Mr Corfield was "very sad" to hear that a body had been recovered "from a deep pool in the River Wye at Builth Wells".
Mr Corfield, a member of Montgomery Young Farmers' Club, was due to meet his family at the Royal Welsh showground where he had been camping with friends.
Speaking at a press conference, his mother Louise Corfield had said on Thursday they were "desperate to know where he is".
Montgomeryshire AM Russell George said the discovery of a body was "incredibly sad news".
"There has been a real feeling of helplessness in the community as people just want to help in some way," he said.
"James and his family are well-known locally and our thoughts are with them at this difficult time."
A body has been found during the search for a man who went missing from the Royal Welsh Show in Powys.