The 201st Silab Corps of the Afghan national army in the east said the incident took place on Thursday in the vicinity of Tagab district.
The Silab Corps officials said the two Taliban insurgents killed in the explosion have been identified as Qari Mahfooz and Bakhtiar.
The Taliban insurgents group has not commented regarding the report so far.
The anti-government armed militant groups frequently use explosives materials for the roadside bombings and car bombings to target the government staff and security personnel.
However, in majority of such incidents the ordinary civilians are targeted besides such bombings incur casualties to the security personnel and in some cases the Taliban militants themselves are killed or wounded.
The United Nations Assistance Mission in Afghanistan (UNAMA) in its latest reported highlighted that 40 per cent of all civilian casualties during the six-month period were killed or injured by anti-government forces using improvised explosive devices (IEDs), such as suicide bombs and pressure-plate devices, which were responsible for the deaths of 596 civilians and injured 1,483.