The attack took place around 10:00 am near a teacher training center in Jalalabad city over a powerful community elder.
Provincial governor spokesman Ataullah Khogyani confirmed the attack, but did not provide further details.
But a hospital source told Ariana News that they have received at least two dead bodies and 10 people wounded as a result of the explosion.
Haji Hayat Khan was one of the most influential public upraising figures in Kot district of Nangarhar province against the Islamic State militants.
No group has claimed the responsibility of the attack yet.