The Taliban denied responsibility for the bombing, which also left 13 people wounded on the eve of a second round of four-country negotiations aimed at restarting peace talks with the insurgents.
The carnage came during a "jirga", an assembly of tribal leaders, at the home of politician Obaiduallah Shinwari, who escaped unscathed.
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Ambulances rushed to the scene, which was littered with pieces of human flesh, sandals and charred debris.
Shinwari is a well-known member of Nangarhar's provincial council and his family is said to be actively involved in local politics.
Afghan President Ashraf Ghani strongly condemned the attack, warning security forces will go after the culprits with "all its strength".
"When terrorists lose the ability to fight face-to-face with our security forces, then they target public places and kill our innocent people," Ghani said in a statement.
"The government will fight those who shed the blood of our innocent people."
The United Nations also condemned the killings, reiterating its plea to all armed groups to stop the deliberate targeting of civilians.
The bombing is the latest deadly attack in the city since Wednesday, when Islamic State (IS) jihadists claimed responsibility for a four-hour gun and bomb siege targeting the Pakistani consulate.
All three attackers and seven members of the security forces were killed in the assault, the first major IS attack in an Afghan city and on a Pakistani government installation.
The group, which controls territory across Syria and Iraq, is making gradual inroads in Afghanistan, challenging the Taliban on their own turf.
The jihadists have managed to attract disaffected Taliban fighters increasingly lured by the group's signature brutality.
In a sign of their growing reach in Afghanistan, the group has taken to the airwaves with a 90-minute Pashto-language radio show called "Voice of the Caliphate".
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