His statement said one of the suspects had confessed to the attack, in which four people supposedly visiting their mother stormed the compound and opened fire in March this year.
An Indian priest was kidnapped, and his fate was still unknown.
The motive for the attack was unclear but President Abd-Rabbu Mansour Hadi called it an act of terrorism.
The spokesman described those arrested as a "gang" but gave no details on their number or motives, and said the search for suspects continued.
Yemen's Saudi-backed government has been forced out of the capital Sanaa by Houthi rebels and is now based in Aden, but struggles to impose its authority even there.
Once a cosmopolitan global seaport, Aden has become a backwater as result of the civil war, and more recently a conflict zone, its Christian community largely driven away.
