The deceased are identified as the three brothers, who were travelling in a vehicle when they struck the IED.
The officials have said that one more person was also injured in the explosion.
No group has commented on the incident so far.
Earlier this week, at least four terrorists belonging to the Islamic State of Iraq and Syria (ISIS), were killed in an airstrike carried out by the security forces in the province.
The airstrike also destroyed several weapons, ammunition, and explosives; the statement added.
Anti-ISIS as well as anti-Taliban operations are underway to eliminate the presence of terrorists in Nangarhar Province and the U.S. forces are providing air force support to the Afghan forces during the operations. (ANI)