In footage posted on YouTube, hooker Hodgson is seen crashing through a closed interior door shoulder first.
The incident reportedly occurred at a student flat in Dunedin on Saturday night, after England had been beaten 16-14 by New Zealand at Forsyth Barr Stadium in their final Four Nations group game, a result that cost Steve McNamara's men a place in the competition's final.
Hodgson, who will play for Canberra Raiders in the NRL from 2015 after agreeing a move from Hull KR, did not feature against New Zealand, having started the previous two matches against Samoa and Australia.
In a statement on behalf of the England team, team manager Jon Roberts said: "We were made aware of an incident that occurred last night around lunchtime today [Sunday]. It is being dealt with internally with the person involved and they will be disciplined.
"The players were given permission to go out after last night's game.
"On behalf of England Rugby League, we apologise for the behaviour and have arranged for the repair of the small amount of damage.
"We have had a great time in Dunedin and the city has made us welcome. Last night's match was a great spectacle for international rugby league and we look forward to returning to the city in the future.​"
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