Col. Ahmed Muse says the bomber struck the 12th April Army Brigade base near the newly reopened sports stadium in Warta-Nabadda district.
There is no immediate word on casualties.
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.