Soldiers had dismounted from a convoy Tuesday in the volatile Panjwaii district when a motorcycle came speeding towards them, military officials said.
When the driver did not heed signals to stop, a warning shot was fired and the motorcycle changed direction and sped away.
Officials say the soldiers then noticed a crowd gathering and discovered that a girl had been shot. Attempts to save her were unsuccessful. Her age was not disclosed.
Three Afghan policemen were injured in a separate incident when Canadian soldiers inspecting a possible explosive device fired on a vehicle that was approaching in the dark with its lights out.
Two members of the Afghan National Police suffered minor injuries, while the third remains in hospital.