Another 40 people were injured, mostly in a stampede that followed the blast in Imphal, the capital of Manipur state, while Hindus were celebrating the birthday of Hindu god Krishna, said police officer Kasim Ali.
The temple belongs to the International Society of Krishna Consciousness, or ISKCON.
The injured included four foreign nationals, an army officer said on condition of anonymity as he was not authorized to talk to reporters.
One of them was an American hospitalized in the Regional Institute of Medical Sciences in Imphal, Chandra Mani Singh, an institute official, told The Associated Press when reached by the phone.
No other details were immediately available.
The attack occurred despite tight police and paramilitary security in and around the temple where hundreds of Hindus congregated for the festival.
No one claimed responsibility for the blast.
Goswami said the attackers escaped after detonating the grenade.
Dozens of insurgencies have festered for years across India's seven northeastern states, of which Manipur is one. Nearly all are fighting for autonomy or independent homelands for the region's indigenous peoples, most of them ethnically closer to Burma and China than to the rest of India.
The militants say the central government in New Delhi - 1,600 kilometers (1,000 miles) to the west - exploits the northeast's rich natural resources while doing little to improve its poor infrastructure and alleviate widespread unemployment.
