Government spokesman Ismael Mukhtar added that university students were among the dead.
The attacker drove his vehicle into the "Ex-control Afgoye" checkpoint, a well-known junction that links the south of Somalia to the capital, Mukhtar told CNN.
Earlier, Mukhtar said the blast also injured at least 60 others.
The attack happened during rush hour in the Somali capital at about 8 a.m. local time, and both civilians and soldiers are among the dead, police say.
Police conduct security searches at the checkpoint, but there is also a taxation office located nearby and the area is heavily populated with civilians and security forces.
Police have warned that the death toll could rise as many of the wounded have been rushed to hospitals.
Two Turkish citizens were among the dead, Turkey's Foreign Minister Mevlut Cavusoglu confirmed shortly after the attack.
"May Allah's mercy be upon our 2 citizens and innocent Somali brothers&sisters who lost their lives in the heinous terrorist attack," Cavusoglu wrote on his Twitter account. He added Turkey would continue to stand with Somalia in the fight against terror.
Al-Shabaab has claimed responsibility for the attack. Since 2006, the Al-Qaeda-affiliated terror group has carried out repeated attacks in Mogadishu against different targets -- killing international aid workers, journalists, civilian leaders and peacekeepers -- as well as Somalia's government and military targets.
It wants to turn Somalia into a fundamentalist state.
Two weeks ago, at least five people were killed after the group attacked a hotel popular with lawmakers and security officials in the Somali capital.
In February, the group claimed responsibility for a car bombing at a crowded shopping mall that left at least 10 dead. It was also behind three car bombings last November that killed at least 52 people with about 100 more injured.