Hashmat Karzai was hosting an event for the Eid al-Fitr holiday at his home in the province when a man posing as a guest set off hidden explosives as Karzai greeted him, the governor’s office said.
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.
“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,” the spokesman said.
There was no claim of responsibility.
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 U.S. troops in the country after most troops leave at the end of 2014.
Ghani, a former World Bank official, condemned the killing of his adviser.
“(We) condemn this act, of the enemies of AFG, in the strongest terms,” Ghani wrote on Twitter.
No one else was killed and security agents were investigating, the governor’s office said.
The two candidates agreed to an audit of all the vote’s cast in a second round run-off after U.S. Secretary of State John Kerry brokered a deal, but the process is moving slowly, bogged down by frequent disagreements.