BAGHDAD—An American teacher at a Christian school run by U.S. evangelicals in Iraq's Kurdish region was shot dead in class by one of his students in a rare incident of its kind.

The killing took place at about 10:30 a.m. Thursday at the private Classical School of the Medes in the city of Sulaimaniya following a heated argument between an American teacher and a Kurdish Muslim student in the 11th grade, said the region's Education Minister Safin Mohsen Dezai.

The...