The governor, Mohammed Ali al-Hasani, was killed when the bomb exploded next to his convoy as it drove through the provincial capital, Samawa, police say.
Several bodyguards were also injured in the explosion, which happened at 0800 local time (0400 GMT).
Mr Hasani belonged to the largest Shia party in Iraq, the Supreme Islamic Iraqi Council (SIIC).
He is the second Shia governor killed this month.
Iraq has 18 provinces.