Wali Karzai said his convoy was attacked by men in Surobi, a mountainous area about 40km from Kabul, as he returned from a trip to the eastern city of Jalalabad.
The provincial governor said the attackers fired rockets and machine guns at the vehicles as they travelled from the Nangarhar province.
He believes he was the target of the attack, because the men fired only at the front of the motorcade, where he was riding.
"I was the target. The attack was against me," he said, but did not say who they might be.
The attack comes three months before Karzai stands for re-election in the war-torn country's second presidential ballot.
Karzai has escaped several assassination attempts himself since he took power after the fall of the Taliban government.