Nasir Ghairat was killed around 9:20a.m. in Qalae Koche Barqi area, Police District 8 of the city, Ferdaws Faramarz, a police spokesman said.
His driver was injured in the shooting, Faramarz said.
Earlier, Mohammad Qasim Khoshiwal, deputy head of provincial council in Logar, said that the attack left four people dead including Ghairat and his three guards.
There was no immediate claim of responsibility for the assault.