The provincial government media office in a statement said the incident took place in Khogyani district late on Tuesday night.
The statement further added that three Taliban insurgents including two Pakistanis were killed during the clash.
At least two civilians were also killed after the militants opened fire on the security forces, the provincial government said, adding that a local police also lost his life and three others sustained injuries.
The anti-government armed militant groups including Taliban militants have not commented regarding the report so far.
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.
This comes as the ground operations and airstrikes are underway in some remote parts of the province against Taliban, ISIS, and other militant groups.