The Ministry of defense (MoD) said the operation was conducted late on Sunday night in northern Kunduz province.
Gen. Zahir Azimi, spokesman for the Ministry of Defense said the operation was conducted in Chahar Dara district which was cleared from the militants presence.
The Taliban shadow governor killed during the operation was identified as Mawlavi Mohammad Ismail, Gen. Azimi said.
He said the operation will continue until the area is completely cleared from the militants activities.
The anti-government armed militant groups have not commented regarding the report so far.
Kunduz is among the relatively volatile provinces in northern Afghanistan where anti-government armed militant groups are actively operting in a number of its districts.
According to Gen. Azimi, the militants were looking to expand their activities in northern Afghanistan by creating sancuatires by their plans were thwarted by Afghan commando forces.