The provincial government media office said the incident took place at around 9am local time in the vicinity of Khogyani district.
The statement further added that an improvised explosive planted in the vehicle of a local Taliban commander went off in a picnic area, leaving the Taliban command dead along with his two companions.
According to the provincial government, the Taliban commander killed in the explosion has been identified as Hakimullah.
At least four civilians also sustained injuries in the explosion, the provincial government said, adding that the health condition of the wounded civilians is satisfactory.
No individual or group has so far claimed responsibility behind the incident.
Nangarhar has been among the relatively calm provinces since the fall of the Taliban regime in 2001 but the anti-government armed militants have been attempting to expand their foothold in this province during the recent years.