Capt. Mohamed Hussein says the toll is expected to rise.
Police Col. Ahmed Muse says the bomber struck the 12th April Army Brigade base near the newly reopened sports stadium in Warta-Nabadda district.
Witnesses say ambulance sirens can be heard as police cordon off the scene. Huge clouds of smoke are billowing.
The al-Qaida-linked al-Shabab extremist group often targets military sites in Mogadishu.