The Briton, who was the head of a shipping company, was killed by a bomb in his car in the Moalla area near a hotel where his company has an office, the official said.
Police did not comment on the motive of the attack.
An intelligence officer told AFP, however, that the attack "carries the fingerprints of Al-Qaeda."
The British Foreign Office confirmed that one of its nationals had been killed in Yemen.
"We can confirm the death of a British national in Yemen on July 20. We are providing consular assistance to the next of kin," a Foreign Office spokesman told AFP.
"The family have requested the media respect their privacy at this difficult time," he added.
He did not identify the victim.
Police did not let journalists approach the site of the blast.
Witness Abdullah al-Sharafi told AFP: "I head the explosion, I hurried there, and I found the car in pieces and a charred body."
Attacks are relatively rare in Aden, which remains generally calm despite deadly unrest in other southern provinces that have seen repeated clashes between suspected Al-Qaeda militants and security forces. (*)
Editor: Kunto Wibisono
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