The Guardian newspaper reported a team member had been held up at gunpoint while returning from a night out and the incident had occurred early on Tuesday.
"There has been an incident of theft involving a Team GB athlete returning to their accommodation," an association spokesman said.
"All members of our delegation, including the individual concerned, are accounted for, and are safe and well," he said, without providing further details.
The incident comes after U.S. gold medallist Ryan Lochte and three team mates said they were robbed by armed men carrying police badges while travelling to the Athletes' Village in a taxi in the early hours of the morning after a party.
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The incidents have stoked concerns about the safety of competitors and visitors to Rio for South America's first Games, which conclude on Aug. 21.
British track and field officials have advised athletes against going into the city, the newspaper said, referencing an email sent to athletes.
"Do not go out of the village wearing TeamGB kit or carry anything of value unless absolutely unavoidable – this makes you too big a target for theft/crime," they told athletes in the email according to the report.
"You MUST inform a member of team management if you are leaving the village and planning on staying out overnight – please do this BEFORE you leave."
"Rio is NOT a safe environment, and the level of crime has spiked in the last few days," the letter said.
"Think very carefully about whether it is worth the risk of leaving the village to celebrate after you have finished competing – BOA/UKA staff cannot guarantee your safety when away from the village/British School/British House.
"Our strong advice is that it is simply not worth the risk given the current climate in Rio."
(Reporting by Karolin Schaps in London; editing by Peter Rutherford/Sudipto Ganguly)
