Ahmad Wali Karzai had left his home in the main southern city of Kandahar just minutes before the blast at around 0650 GMT on Tuesday.
Two fire engines were fighting a blaze started by the explosion and about 50 police were keeping people away from the house, a journalist with French news agency, AFP said.
Two injured people were seen being taken from the house.
Tuesday’s explosion came one day after 10 Afghani policemen, including a police chief were killed by Taliban fighters in a province south of Kabul.
At least 90 people have been killed in violence this week.
Abd Al-Khaliq, police chief of Logar province, and several other senior police officers from the province were among those killed in an ambush in Kharwar district on Monday, Logar’s military commander, Dr Fazl Allah Mojadidi, told the Reuters news agency.
Police said they believed the attackers were Taliban loyalists.