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The attacker was also shot dead after the incident, which comes following a string of recent attacks on Afghanistan's security forces by people in military uniforms, the ministry said.
"One person fired, another person has been killed, another person has been injured. We don't have full details yet," said spokesman Mohammad Zahir Azimi.
The gunman was in military uniform and was shot dead after the incident, the spokesman said.
It was not immediately clear whether the shooting was a spat between soldiers which got out of hand or an insurgent attack.
Local media reported that the person initially shot dead was a soldier.