Karzai's candidate for first vice-president, Ahmad Zia Masud, was not injured in the attack on Wednesday.
The blast hit Masud's convoy as it was travelling from the airport to the rally site at Faizabad, the capital of Badakhshan province in northeast Afghanistan.
"In a bomb explosion at Ahmad Zia Masud's rally two people were killed and two were injured today before noon," interior ministry spokesman Lutf Allah Mashal said.
"Ahmad Zia Masud is sound and safe," he added.
No one has been arrested so far.
"The investigation is going on. It is the work of the enemies of peace and the elements who want to derail the election process," Mashal said.
Ahmad Zia Masud is the brother of Ahmad Shah Masud, the renowned fighter against the Soviet occupation in the 1980s and of the later struggle against the Taliban regime.
The bomb blast was the latest in a series of attacks in the run-up to Afghanistan's first presidential election on Saturday.
Officials have warned of a possible sharp rise in attacks on election day when up to 10.5 million registered voters go to the polls, with major cities at risk of car-bomb blasts and polling stations under threat of armed assault.
Nearly 60,000 Afghan police and soldiers backed by 27,000 international troops will be in position to protect the 5000 polling stations throughout the country.