The deputy provincial governor says the commander, identified as Abdul Rauf, was killed along with four other militants when a drone-fired missile struck their car.
Afghanistan's intelligence service issued a statement saying the suspected Islamic State commander was among six people killed in the strike, which it said was carried out by Afghan forces.
The Islamic State group, which controls a third of Syria and Iraq, has a small but growing presence in parts of Afghanistan, officials and tribal sources told The Associated Press last month. They said a man known as Mullah Abdul Rauf was actively recruiting fighters for the group.