Abdullahi Mohamed Ali has told the BBC.
State media named the suspect as Amar Ibrahim and said he was also a member of the al-Shabab group, which recently vowed to join al-Qaeda’s global jihad.
Officials said he had replaced a militant in the al-Qaeda hierarchy who had been killed by the US in September.
Al-Shabab, which controls much of southern Somalia, denied the claims.
Mr Ali confirmed to the BBC that an al-Qaeda fighter had been killed, but did not name him and said the government “would provide evidence later”.
State media said Ibrahim had replaced Kenyan-born terrorism suspect Saleh Ali Saleh Nabhan as al-Qaeda’s man in Somalia.
US agents had hunted Nabhan for years over attacks on a hotel and an Israeli airliner in Kenya in 2002, before killing him in a helicopter raid last September.
The US long accused al-Shabab of being al-Qaeda’s proxy in the region, but al-Shabab had denied the links until last month when it released a statement promising to “combine” its local jihad with al-Qaeda’s global fight.
Somalia has been wracked by violence for much of the past 20 years. It has not had a functioning central government since 1991.