Hashmat Karzai was hosting an event for the Eid al-Fitr holiday on Tuesday when a man posing as a guest set off explosives hidden inside his turban.
"A suicide bomber disguised as a guest came to Hashmat Karzai's house to greet him," Dawa Khan Minapal, the Kandahar provincial governor's spokesman, told AFP.
"After he hugged Hashmat, he blew up his explosives and killed him."
Hashmat Karzai worked in this year's presidential election campaign for Qayyum Karzai, the president's brother, and later moved to support Ashraf Ghani when Mr Qayyum withdrew from the race.
Mr Ghani, a former World Bank official, has condemned the killing of his adviser.
"(We) condemn this act, of the enemies of AFG, in the strongest terms," Mr Ghani wrote on Twitter.
No one else was killed and security agents were investigating, the governor's office said.
There has been no claim of responsibility for the attack.
The incident comes as the country is caught in a political deadlock over a disputed election to replace Hamid Karzai as president.
Ashraf Ghani and his rival Abdullah Abdullah both claim victory in the June 14 run-off election, which has been mired in allegations of massive fraud.
Mr Ghani won the vote according to preliminary results, but an audit of the ballots is under way after Mr Abdullah refused to accept defeat due to fraud claims.
The new president is due to be sworn in next month.
Major delays could complicate plans for an agreement to keep about 10,000 US troops in Afghanistan after most troops leave at the end of 2014.