Teenagers were lining up at the base's gate on Sunday when the attacker detonated their explosives, they said.
A military captain who gave his name as Suleiman described the attack as he had seen it unfold.
"I was on the other side of the road. A speeding tuk-tuk stopped, a man alighted, ran into the queue, and then blew himself up. I saw 10 people dead, including recruits and passers-by. The death toll may rise," he said.
Dozens of abandoned shoes and the remains of the suicide bomber were visible at the scene.
Another witness, Abdisalan Mohamed, said he had seen "hundreds of teenagers at the gate as we passed by in a bus".
"Abruptly, a deafening blast occurred, and the area was covered by dense smoke. We could not see the details of casualties," he said.
Medical staff at the military hospital told Reuters they had received 30 injured people from the blast and that six of them had died immediately.
Government forces quickly cordoned off the entire area.
In a statement on Sunday Islamist militant group al Shabaab said it was behind the attack and that it had killed as many as 30 soldiers and wounded 50 more. Government officials could not immediately be reached for comment.
Al-Qaeda-linked al Shabaab has waged an insurgency in Somalia since 2007, and has recently been battling the army to extend gains in central Somalia.
The attack echoed a similar incident in 2023 when a suicide bomber killed 25 soldiers at the Jale Siyad base, located opposite the Damanyo facility.
Sunday's attack followed the assassination on Saturday of Colonel Abdirahmaan Hujaale, commander of battalion 26, in the Hiiran region, after local reports of al Shabaab militant infiltration into government and security forces.
