Quoting the Africa Review, the News Agency of Nigeria reports that Al Shabaab militants shot dead the governor and his brother.
The two were visiting a relation in the area when the gunmen, who are said to have trailed them, opened fire.
Eyewitnesses said the gunmen fled the scene before policemen arrived.
The Islamist Al Shabaab fighters has reportedly claimed responsibility for the attack.
The incident occurred a few hours after a bomb exploded at the city centre, killing at least three civilians and injuring several others.
A saloon car packed with explosives blew up along the Maka-alMukarrama Avenue, near Dar-ul-Shifa hospital, at around 6:30pm. The blast was reportedly heard across the city.
It was the second bombing within a week, following a deadly blast that killed at least 10 persons along the same avenue on Sunday.
Early Friday, Al Shabaab retook Leego in the Lower Shabelle region after African Union troops (Amisom) withdrew from the town.
Ibrahim Adam Najah, the governor of Lower Shabelle in the south of the country, told local media that the militants took over the town minutes after the Amisom soldiers left.
Leego is about 130 km northwest of the capital Mogadishu.
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