Ahmad Khan Samangani, an ethnic Uzbek MP, was attending a wedding party for his daughter in the provincial capital, Aybak, when the blast happened.
The attacker, posing as a guest, embraced Mr Samangani before detonating his explosives, a witness said.
A Taliban spokesman denied involvement in the attack.
Ahmad Khan Samangani was a commander in the mujahideen militia during Afghanistan’s civil war in the 1980s.
He was known as a supporter of President Hamid Karzai and a rival of Gen Abdul Rashid Dostum, a powerful civil war commander in the north and currently one of Afghanistan’s most prominent Uzbek politicians, the BBC’s Bilal Sarwary, in Kabul, says.
Mr Samangani became a member of parliament last year, replacing one of several sitting MPs expelled by the Independent Electoral Commission for alleged electoral fraud in the 2010 parliamentary election.
Taliban spokesman Zabiullah Mujahid issued a swift denial of responsibility for the attack that killed Ahmad Khan Samangani, who had made many enemies during his years as a militia commander.