Acting provincial governor for Nuristan province Hafiz Abdul Qayum confirmed the report and said the district police chief was killed in an ambush in eastern Laghman province.
He said Enayatullah was on his way to his house when the militants ambushed him in Alingar district, leaving the police chief dead and his driver wounded.
No group including the Taliban militants has so far claimed responsibility behind the attack.
This comes as the Taliban led insurgency has been rampant during the recent months across the country despite efforts to end the ongoing violence through reconciliation process.
Laghman and Nuristan provinces are among the relatively volatile provinces in eastern Afghanistan where anti-government armed militants are active in a number of its districts and often carry out insurgency activities.
The Taliban militants have recently attempted to carry out deadly attacks on government institutions in this province but the attack plots were foiled by the security forces.
The Afghan intelligence operatives arrested a would-be suicide bomber before he carry out an attack in a busy part of Mehtarlam city late last month.