A police spokesman said the security personnel had attempted to halt the vehicle as it approached the checkpoint at speed.
The al-Shabaab Islamist terrorist group claimed responsibility.
Another attack in the same area a short time later had been thwarted, police said.
Acting on a tip-off, security forces had found a car packed with explosives and carried out a controlled detonation, it said.
At the weekend, a remotely detonated bomb claimed 11 lives in a Mogadishu restaurant.
Al-Shabaab has claimed responsibility for all the attacks.
The militia controls areas in parts of Somalia, but in recent years it has been pushed back from the capital.
However, there are repeated attacks in Mogadishu on government facilities and on hotels and restaurants, where the Islamists condemn the Western lifestyle that prevails as un-Islamic.
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