Five more were injured in the incident which happened at 8:30 in the morning. The injured including three women were all civilians, according to Abdul Ghani Musamim, a spokesman for provincial governor.
The attack killed head of human resource department, Sangar Afghan, and the provincial manager of Afghanistan Telecom Regulatory Authority, Mohammad Nasir, according to local officials.
There was no immediate claim of responsibility for the attack, but officials blamed the Taliban.
Kunar lies near the border with Pakistan and is considered one of the volatile provinces.
Deadly clash between IS and Afghan forces in Kunar
In a separate incident in Kunar, a deadly clashed happened between Islamic State militant group fighters and Afghan forces, officials said.
At least 25 were killed in the clash which took place in Chapa Dara district after the insurgents targeted police and army posts.
The dead included 21 insurgents and 4 Afghan forces, according to Juma Gul Hemat, the provincial police chief.
The battle also left 23 injured, including 17 insurgents and six forces.