According to Abna, the bomb had been planted behind the mosque’s Mihrab (a niche in the wall of a mosque, at the point nearest to Mecca, toward which the congregation faces to pray).
The blast happened on Sunday night at Imam Baghir (AS) Mosque when worshippers were saying their Maghrib prayers.
Molla Ramezan Sarvari, the prayer leader, was severely injured in the bomb explosion and later succumbed to his injuries at the hospital, local sources said.
A woman was among those injured in the incident.
There have been no claims of responsibility so far.
Police have launched an investigation to identify those behind it.
Herat Governor Mohammad Asif Rahimi condemned the act of terrorism, blaming it on those who seek to foment sectarianism in the region.
Shia Muslims have been targeted in terrorist attacks and large-scale kidnappings across Afghanistan in recent years, which have prompted demonstrations and sit-ins in Kabul and elsewhere.
The rise of Daesh (ISIL) in Afghanistan has also triggered concerns in a country which has been torn apart by decades of Taliban-led militancy and the 2001 invasion of the United States and its allies.