The bomber detonated his explosives as the elders gathered to seek aid for war-displaced families in Jalalabad, the capital of Nangarhar province which is a hotbed of IS militancy.
The group appears to be intensifying attacks against the government and civilians as Afghan forces, backed by NATO air strikes, step up anti-IS operations in Nangarhar.
"Six civilians were killed and six others were wounded in the suicide attack on a gathering of elders in Jalalabad," provincial spokesman Ataullah Khogyani told AFP.
A police spokesman confirmed the toll, adding the wounded had been taken to hospital. The powerful bomb ripped through the facade of the building, leaving it littered with shredded debris.
"Terrorist groups can give people nothing other than destruction, death and fear," President Ashraf Ghani said in a statement, condemning the carnage.
"Terrorists will never succeed in their ominous mission to destroy the country."
The Syria-headquartered Islamic State group claimed responsibility for the attack in a statement, adding the bombing left 15 people dead and 25 others wounded.
Insurgent groups in Afghanistan are known to exaggerate battlefield claims.
Taliban fighters are active in Nangarhar, but the province also faces an emerging threat from IS loyalists who are making gradual inroads in Afghanistan.
Last week, militants linked to IS jihadists abducted and killed around 30 civilians, including children, in the central province of Ghor, raising concerns about the group's expanding presence beyond its eastern stronghold.
IS fighters have been trying to spread the group's footprint beyond Nangarhar, winning over sympathisers, recruiting followers and challenging the Taliban on their own turf.
The Afghan government is currently in the middle of an operation, backed by NATO airstrikes, against IS in Nangarhar.
NATO recently said the group's influence was waning as it steadily lost territory, with fighters largely confined to two or three districts in Nangarhar from around nine in January.
"Right now we see them (IS) very focused on trying to establish their caliphate... inside Afghanistan," John Nicholson, the top US and NATO commander in the country, told reporters recently.
In July, IS jihadists claimed responsibility for twin explosions that ripped through crowds of Shiite Hazaras in Kabul, killing at least 85 people and wounding more than 400 others.
The bombings marked the deadliest single attack in the Afghan capital since the Taliban were ousted from power in a 2001 US-led invasion.
