Army spokesperson Lt Gen Asim Bajwa in a statement last night said the man hanged by the militants was neither a soldier nor an intelligence official.
In the video footage released on Sunday, the militants were shown hanging a man who identified himself as belonging to a Pakistan army unit and said he worked as a spy.
The army said that the executed man was an Afghan national who was kidnapped for ransom and killed when his family failed to pay the money demanded by the militants.
Pakistan lifted self-imposed moratorium on death penalty after militants attacked a school in Peshawar in December and killed 150 people, mostly children.
About 240 convicts have been executed in Pakistan since December.