Al Jazeera's James Bays, reporting from the Afghan capital, Kabul, said the Taliban had claimed responsibility for the attack.
"The Taliban spokesman has spoken to Al Jazeera and the Taliban say they ambushed the convoy," he said.
"A ministry of interior spokesman has told Al Jazeera that Fahim was uninjured in this attack but he says that one of his bodyguards was injured as was a TV cameraman who was travelling with the vice-presidential hopeful's convoy."
Bays said that the attack raised new questions about the level of security for candidates ahead of the election.
"Fahim was travelling in northern Afghanistan, normally seen as one of the more stable parts of the country," he said.
"There is security for candidates. [But] it's very, very hard for the security teams because these convoys are travelling on very small roads in remote areas."
The ambush came a day after a suicide attack on a police headquarters and courthouse in the eastern city of Khost.
The Afghan interior ministry said seven suspected Taliban suicide bombers dressed in women's burqas carried out the attack on Saturday with rocket-propelled grenades and AK-47s.
A candidate in Afghanistan's upcoming presidential election was in one of the buildings at the time of the attack, but escaped unharmed.
A Taliban spokesman claimed that the attackers were targeting the courthouse rather than Ramazan Bashardost, a former planning minister.
With growing violence across large parts of the country and Afghan and international forces seemingly unable to ensure security, there are fears that few voters will turn out for the August election.
But the US special envoy to Afghanistan and Pakistan has said he is sure that voting will go ahead in the country's most dangerous areas, although "complex challenges" remain.
"There will be voting in the south, that I can assure you," Richard Holbrooke told a news conference in Kabul on Saturday.
Karzai, the incumbent president, is a clear front-runner ahead of 38 challengers.