Trelawny, who presents "Music Matters," "In Tune" and "Live in Concert" for BBC radio stations, slipped and fell while in police custody Thursday and exacerbated a recurring shoulder injury, Britain's The Guardian reported.
"He put his shoulder out and today they're putting it back in under general anesthetic. He told me that himself. He has a history of problems with that shoulder," said Bruce McDonald, administrator of the Zimbabwe Academy of Music.
McDonald said Trelawny was cheerful and was to fly back to Britain Monday.
Trelawny was hosting a music festival in Bulawayo at the the time of the incident, though the BBC denies he was attending the event as a representative of the news organization.
"We are aware of the situation and hope it will be resolved as quickly as possible," a BBC spokesman said.