Capt. Mohamed Hussein said bodyguards escorting Nur Farah opened fire on a car carrying Abbas Abdullahi, the public works and reconstruction minister, near a checkpoint close to the palace.
It is not immediately clear what prompted the shooting. Security concerns are high in Somalia's capital, Mogadishu, as the al-Shabab extremist group continues to target the palace, military facilities and hotels with suicide car bombings and other attacks.
The car carrying the minister approached and trailed the car carrying the auditor general, promoting his bodyguards to open fire, Hussein said.
Somalia's new cabinet was sworn in in late March after President Mohamed Abdullahi Mohamed was elected in February.
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The minister who was killed, a former refugee who spent large parts of his life at a camp in Kenya, had been the youngest member of Somalia's new cabinet.
Somalia's information minister, Abdirahman Omar Osman, sent condolences over the death, calling Abdullahi a "brilliant and rising young star who showed commitment in serving his country."
The new president has vowed to improve security in this Horn of Africa country, which has seen a quarter-century of chaos.
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