No militant group has so far claimed responsibility for the ongoing assault and no fatalities were immediately reported.
Indian foreign ministry spokesman Vikas Swarup told AFP: "Our consulate has been targeted but everyone is safe."
A shopkeeper near the consulate told AFP he saw several injured people lying around the area after a "big boom" shattered his windows.
The area, also home to other diplomatic missions, has repeatedly come under attack in recent months.
In January Daesh (ISIL) claimed responsibility for a deadly gun and bomb siege targeting the nearby Pakistani consulate in Jalalabad, the first major attack by the group in an Afghan city.
Nangarhar, of which Jalalabad is the capital, faces an emerging threat from loyalists of Daesh, which controls territory across Syria and Iraq and is making gradual inroads in Afghanistan -- challenging the Taliban on their own turf.
The attack comes as direct peace talks are expected to start this week between the Afghan government and the Taliban.