McCarthy, a 22-year-old midfielder for the Australian Football League club, had been on holiday with a group of team-mates before he was found dead outside the Flamingo Hotel early on Sunday morning, local media reported.
"We were informed at 9:30 (00:30 Monday UK time) this morning that John had been involved in a fatal accident," Port CEO Keith Thomas said in Adelaide.
"It's our understanding that at the time of his death he wasn't with any other players."
Local media quoted a spokesperson at the hotel as saying his body was found on the hotel's driveway, after an apparent fall from a balcony. The spokesperson was unavailable for comment when contacted by Reuters.
McCarthy was taken to a nearby hospital where he was pronounced dead, reports said.
Thomas said neither McCarthy, nor any of the other players, had been staying at the Flamingo.
"It's a tragedy, but we can't really say anything more than that at this time," a club official told Reuters.
The death has cast a pall over the AFL's postseason finals series which opened over the weekend. Port Adelaide failed to make the finals in the 18-team competition and played their last regular season game on September 2.
McCarthy had played 21 games in a breakout season with Port this year after struggling to make the first team at Melbourne-based rivals Collingwood.
Players of the bruising indigenous code traditionally embark on wild celebrations with team-mates in their home cities and in overseas destinations after their final games of the season.
The blowouts, which have been dubbed 'Mad Mondays', have attracted negative headlines in recent years with some pundits blasting clubs for failing to protect their players.