The child is now in a serious condition in hospital after the incident around 2pm in Walton, Liverpool.
The crossbow was seized by police and is now being examined.
No arrests have yet been made, and police believe she may have been injured in an accident.
An eyewitness told the Liverpool Echo: “I could see police carrying bin bags out to the back of a van.
“It’s normally very quiet so such a big police presence was worrying.”
Detective Inspector Sabi Kaur said: “This incident shows the obvious dangers posed by firearms stored in Merseyside.
“We will continue to listen to all of the information we receive to help us identify and remove these weapons from the streets.”
He added: “I am sure the community in Walton will share our shock and distress at the fact a child could have been hurt in this way.
“Our enquiries into this incident are at a very early stage, and we are still trying to establish the full facts but we know it was an isolated incident.”
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