Hashmat Karzai was hosting an event for the Eid holiday at his home in the province when a man posing as a guest set off hidden explosives as Mr Karzai greeted him.
The attack comes as the country is caught in a political deadlock over a disputed election to replace Hamid Karzai as president.
A spokesman for the provincial governor said the bomber had been well dressed, adding: "His style was very modern, everything was new, and when he came to talk with Hashmat Khalil and wish him a happy Eid, he blew himself up."
No groups have admitted ordering the killing.
Mr Ghani, a former finance minister, and his rival, former foreign minister Abdullah Abdullah, say the vote was marred by fraud, and the United Nations has sent a team of observers to oversee an audit of the ballot.
The new president had been due to be sworn in next month.
Major delays could complicate plans for an agreement to keep about 10,000 American soldiers in the country after most troops leave at the end of 2014.
Mr Ghani, a former World Bank official, condemned the killing of his adviser, saying: "We condemn this act in the strongest terms."