-led coalition warplanes have been carrying out air strikes in the area, targeting militant hideouts, for three days.
The elite Counter Terrorism Service and the military’s operations command for Diyala province did not name the commander but they said in a statement he was in charge of Islamic State forces in Hamrin.
He and four “followers” were killed in the area northeast of Baquba, the provincial capital, on Sunday, it said.
Iraq declared victory over the group, which once held large swathes of the country, in December 2017.
With its dream of a caliphate in the Middle East now dead, Islamic State has switched to hit-and-run attacks aimed at undermining the Baghdad government.
The militants regrouped in the Hamrin mountain range in the northeast, which extends from Diyala province, on the border with Iran, northwest to the River Tigris in Kirkuk province.
Reporting by Adam Hadi; Writing by Ahmed Aboulenein; Editing by Angus MacSwanOur Standards:The Thomson Reuters Trust Principles.