Kent Police were alerted to reports of a disturbance on the Isle of Sheppey on August 2.
Officers launched the drone as part of their response to the report.
The remote-controlled aircraft hit an overhead cable in the air, which caused it to fall to the ground.
A child suffered a serious injury to their hand as a result.
The Independent Office for Police Conduct (IOPC) has launched an investigation into the incident.
A spokesperson for the police watchdog said: “We can confirm we are independently investigating an incident where a child was hurt by a drone which crashed while being flown by Kent Police.
“It happened on 2 August when officers were responding to reports of a disturbance on the Isle of Sheppey.
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“A drone was launched, hit an overhead cable and fell to the ground, hitting the child and seriously injuring their hand.
“As part of the on-going investigation we have served a misconduct notice on a special inspector.
“The serving of a notice does not necessarily mean disciplinary proceedings will follow.”
