King's Lynn Aero Modelling Club (KLAMC) launched an investigation into the incident on Wednesday afternoon.
Firefighters were called after a model aircraft became stuck up a tree near the A148 at Roydon Common.
Firefighters feared it could fall onto a passing vehicle. A turntable ladder was sent to the scene while police officers were also called out to direct the traffic.
The flier had lost control of the battery-powered polystyrene or 'foamy' plane, which was being flown over KLAMC's airfield on the common.
Club spokesman Steve Bennington said: 'We strictly don't overfly the road so we're investigating this thoroughly with the person concerned. They've been severely reprimanded.
'As I understand it, the chap was flying someone else's aeroplane, acting as an instructor.'
The 70-strong club has a runway and wind sock on the common, where members fly their planes. Mr Bennington said the incident was the first to have involved the emergency services in the its 25-year history.
He added it had procedures for retrieving members' aircraft which became lodged in trees and did not advise fliers to dial 999.
'I don't think this was the appropriate course of action,' he said. 'It could have been retrieved without involving the emergency services.'
Members are advised to call the club's safety officer, who frees aircraft lodged in trees using a telescopic fishing pole. Mr Bennington said the pilot had been warned he faced expulsion if a similar incident occurred.
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