The Jalalabad-Kabul road is regularly a scene for attacks due the the large number of compounds and military bases alongside it.
The attack came hours after two mortars hit the presidential palace in Kabul and the police headquarters nearby. No casualties were reported.
Zabihullah Mujahid, a Taliban spokesman, said the group was responsible for the both the rocket attacks and that on the convoy.
James Bays, Al Jazeera's correspondent in Kabul, said there was a fear of further suicide attacks in the capital.
"Intelligence sources are telling Al Jazeera they have some information that maybe there are more suicide bombers hidden in the city," he said.
"They're trying to stop anyone else coming in, they are searching a lot of the cars [coming into Kabul], but they fear that some may already be here."
Election workers killed
In Afghanistan's usually peaceful north, attacks killed five people, including an election candidate and three electoral workers.
A roadside bomb ripped through a vehicle in the northern province of Badakhshan, killing three electoral workers, including the district's election chief, and their driver.
In a separate attack in the northern Jawzjan province, Abdul Rahim, a provincial candidate in the elections, was killed in a Taliban ambush.
Six rocket attacks were also reported in Jalalabad, in the east, injuring at least nine people, including four children, and a suicide bomber attacked a military post in the southern Uruzgan province, killing five - three Afghan soldiers and two civilians.
In Paktia province, a school being used as a polling station was burned down by the Taliban, but no one appeared to be hurt in the attack.
Alarmed by the attacks, the government appealed for a local and international media blackout on reporting violent acts on polling day.
The Taliban have vowed to disrupt the August 20 elections, in which 17 million people are eligible to elect a president and 420 councillors across 34 provinces.
They have demanded that Afghans boycott the polls, threatening to cut off the fingers of those who vote and saying they will attack polling stations.
Marwan Bishara, Al Jazeera's senior political analyst, said that the elections would be a key test in the fight between the US and the Taliban.
"The idea of elections, within a comprehensive American strategy, is meant to underline that Afghanistan has minimum stability, has minimum security and has minimum commonality of thought that unites the country," he said.
"But the Taliban is trying to do exactly the opposite. It is trying to show that there is no stability in the country - that it is divided and lacks security."
Opinion polls are showing a lead for Hamid Karzai, the incumbent president, with 45 per cent of the ballot, but not an outright majority.
|Violence has increased in the run-up
to the polls [Reuters]
He has gained the support of tribal chiefs and leaders of armed groups who fought in Afghanistan's civil war.
But without an outright majority, Karzai would be forced into a run-off with his closest challenger, predicted to be Abdullah Abdullah, his former foreign minister.
Nato-led forces have said that all offensive military operations will be suspended during the elections, with only operations considered essential to protect the population being carried out.
Afghan security personnel are under similar orders from Karzai.