Crawley was verbally abused and punched by the assailant, who was drunk, causing him to fall to the ground, sustaining cuts and bruises to his face.
Crawley did not attend yesterday's final day of England's tour match with Queensland, which the tourists won by one wicket, but his injuries will not affect his contention for a Test place.
The tour manager, Graham Gooch, spoke to Crawley yesterday about the incident. After lengthy discussions, England have decided not to inform the police and will not be taking further action.
Gooch said: "John was naturally upset by the matter, but other than the cuts and bruises to his face, he is fine and fully fit. We considered informing the police, but John is keen to put the matter behind him and concentrate on the forthcoming Test match."
Gooch added: "We would also like to place on record our thanks to the people of Cairns as, aside from this one unfortunate incident, we thoroughly enjoyed our stay there and received excellent hospitality."
England flew out of Cairns to Brisbane yesterday before the first Test, which starts on Friday, and will train at the Gabba for the first time this afternoon.