Kerow said the injured had been taken to hospital and the fighting had stopped shortly afterwards.
"This kind of clash among the government troops is unfortunate and has been repeated so many times, claiming the lives of nearly 100 troops since January," he said.
Ten civilians were wounded and one of them later died, Ali Muse Abdi, the coordinator of ambulance services in Mogadishu, told Reuters.
Somalia has had no effective government for 19 years and Western nations and neighbours say the country is used as a shelter by fighters planning attacks in East Africa and further afield.
Members of Al-Shabab, Somalia's armed anti-government group, have been fighting to topple Somalia's African Union-backed government, which is led by Sharif Ahmed, the president.
More than 21,000 civilians have been killed since the start of the violence.
The country's Transitional Federal Government controls only a few blocks of Mogadishu with the help of African Union peacekeepers.