It said Ali Essa Ahmed, described as a dual Sudanese-British citizen, last month reported to police that "he had been harassed and beaten up by UAE national football fans for cheering the Qatar team", at the Asian Cup finals.
The UAE, along with Saudi Arabia, Bahrain and Egypt, cut all ties with Qatar in June 2017 over allegations that the energy-rich state supports Islamic extremists.
The embassy said police took Ahmed to hospital "where a doctor who examined him concluded that his injuries were inconsistent with his account of events and appeared to be self-inflicted".
As a result, on January 24, "Mr Ahmed was charged with wasting police time and making false statements", the embassy said.
"We are advised he has since admitted those offences and will now be processed through the UAE courts," said a statement posted online.
It said the British embassy in UAE had been contacted and "due process has been followed", adding that Ahmed speaks Arabic "and fully understands the situation he has put himself in".
"He was categorically not arrested for wearing a Qatar football shirt. This is instead an instance of a person seeking media attention and wasting police time."
The Guardian newspaper reported that the man, named as Ali Issa Ahmad, 26, had travelled to the UAE for a holiday and attended an Asian Cup match between Qatar and Iraq on January 22, where he wore a Qatar shirt.
The Foreign Office in London said: "We are providing assistance to a British man arrested in the UAE, and are in touch with the local authorities."
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