The assailant fatally shot Mohammed Wahab, said officer S. Roopasinghe of the Kalmunai town police department. The Defense Ministry in Colombo confirmed the killing and said it was investigating who was responsible.
Another man, identified as Mohammad Noor, also was hit by gunfire and was admitted to a local hospital.
Kalmunai, about 220 kilometers (140 miles) east of Colombo, is a Muslim-majority area.
The separatist Tamil Tiger rebels, who are mostly Hindus, carried out systematic killings of Muslims in the area during nearly two decades of civil war, reports the AP. I.L.