The masked arsonists torched St Joseph, a Roman Catholic church in the central Crater neighbourhood of the port city, which is controlled by loyalists of the exiled government.
A security official said the attackers could be militants of Al-Qaeda.
"The church is in flames," resident Moetaz al-Maysour told AFP, adding that "masked men started the fire."
Yemen's population is 99 per cent Muslim.
Of the 22 churches that operated in Aden when the city was a British colony before 1967, only a few remain open, used rarely by foreign workers and African refugees.
The jihadist network's Yemen branch, regarded by Washington as its deadliest, has exploited the fighting to boost its presence in swathes of the south and east.
