Defence Minister Abdul Rahim Wardak had just left Kabul airport on Saturday by helicopter when his empty car was fired on by four men in combat uniform.
Ministry spokesman General Mohammad Zahir Azimi said on Sunday that the vehicle was caught in crossfire between two groups of feuding Afghan soldiers.
"At the beginning we thought it was an attempt on the minister's life," Azimi said. But further investigations revealed it was an accident, he added.
"At the same time as the minister's vehicles were passing by, a group of Afghan National Army soldiers fired at each other over a dispute which they had from previous days," Azimi said.
He did not elaborate on the nature of the dispute between the soldiers guarding the airport but said nine of them had been arrested and were being questioned.