The vice presidential hopeful, Ahmed Zia Massood, escaped unharmed, said Khaleeq Ahmed, a spokesman at the presidential palace, but the former governor of Badakhshan, where the attack occurred, was among those injured.
CBS News Correspondent Lara Logan reports Massood was injured, and two other people were killed in the attack.
Mutaleb Beg, a local police official, said one person was killed and several others injured. Another official, Badakhshan criminal department chief Fazel Ahmad Nazari, put the number of injured at five. He said Massood was returning to Kabul by plane.
The convoy was apparently attacked by a roadside bomb or land mine set off by remote control as it passed along a road in Faizabad, the provincial capital, Ahmed said.
The attack came on the last day of campaigning for Saturday's landmark presidential elections, as Massood was traveling from the airport to a campaign rally, and as the United Nations declared the nation ready to hold the vote. Karzai addressed a throng of about 6,000 people at Kabul's sports stadium, telling the crowd that their vote would lay the "first bricks in a wall of democracy" in this war-shattered nation.
"It is clearly the work of people who do not want to see the election take place, and who want to send a message to the international community that this is not a stable environment and that a free and fair election cannot be held here," reports Logan.
The U.S. Embassy, meanwhile, warned that the threat of attacks ahead of the election was high.
"In the run-up to the Oct. 9 elections, potential continues to exist for demonstrations, riots, bombings, and other violent actions against U.S. citizens and interests in Kabul and the rest of the country," it said, urging extreme caution.
The area where Massood's convoy was attacked is not considered a haven for Taliban rebels and had been relatively peaceful in the past. It is, however, a center of Afghanistan's booming opium and heroin trade, with countless poppy fields dotting the landscape.
Ahmed, the palace spokesman, would not comment on who might be behind the attack, but said whoever it is would not succeed in derailing Saturday's vote.
"The elections will continue 100 percent. We knew from day one that as we got closer to the elections, the enemies of Afghanistan would try to disrupt them, but they will not succeed, ever," he told The Associated Press.
Ahmed Zia Massood is the brother of slain Northern Alliance commander Ahmed Shah Massood, who was executed in Kabul in a terrorist attack two days before Sept. 11, 2001, "so it is quite symbolic that they have chosen to target him in this particular attack," reports Logan.
Karzai selected him as a running mate over current Vice President and Defense Minister Mohammed Fahim, a Tajik faction leader.
In Kabul, the special representative for Afghanistan of U.N. Secretary-General Kofi Annan said that despite many problems, the election will be fair enough to give Afghanistan's next ruler legitimacy.
"It is ... with full knowledge of the difficulties that surround this exercise that we deem the degree of freedom and fairness adequate to allow the will of the Afghan people as a whole to translate at the polls, and the next president of Afghanistan to claim to represent the nation," said Jean Arnault.
Speaking at Kabul's battle-scarred sports stadium, used as a public execution ground by the hardline Taliban regime until their ouster in 2001, Karzai urged the crowd to take part in the election.
"Your vote will elect a president for the next five years, but it will do much more than that as well," Karzai told the throngs. "By voting you are laying the first bricks in a wall of democracy that will last for decades and centuries in our country."
Afghanistan's revered former king, Mohammed Zaher Shah, also urged his countrymen to vote, saying they should let their conscience decide which candidate they select.
Some 6,000 people came out to hear Karzai speak, banging drums and shouting slogans like "Long Live Karzai!" and "Karzai is the future!"
Karzai is the overwhelming favorite to win Saturday's vote against 17 challengers, and he hopes the victory will add teeth to his often limited control of the vast, barren country. He has said his main goals are to carry on with reconstruction and curb the power of warlords who still hold sway in much of Afghanistan.
During Taliban rule, the concrete sports stadium was the preferred execution ground for criminals and other outlaws, and the public was encouraged to attend the bloody spectacles. Its transformation into a place of democratic rallies is a dramatic example of how far the nation has come in the three years since a U.S.-led bombing campaign ousted the religious militia.
But the stadium is still pocked with thousands of bullet holes from a quarter-century of war, particularly the internecine feuds that leveled much of Kabul in 1992-1996, and stands as one of countless examples that the nation is still a shell of its former self.
Abdul Habib, a 60-year-old mechanic who was in the crowd, said he could remember the time when the same field was used for executions, carried out with a sword or a shot to the head. Criminals who were not killed often had their hands or feet cut off. Women were shot under their all-enveloping burqas, sometimes for no greater crimes than alleged adultery.
Karzai's rally was held before the attack on Massood, but even so it took place under extremely tight security. The ubiquitous machine-gun wielding U.S. bodyguards and Afghan commandoes that protect Karzai were everywhere, as were hundreds of Afghan soldiers who lined the routes in and out of the stadium grounds.
It was at least the third attack on Karzai and his supporters since campaigning began on Sept. 7. Karzai survived a rocket attack on his helicopter on Sept. 16 as he was on his way to a campaign stop in the southeastern city of Gardez.
Four days later, a roadside bomb in northern Afghanistan hit a convoy carrying Nayiamatullah Shahrani, one of four of Karzai's current vice presidents, injuring one of their bodyguards without harming the politicians, police said.