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New South Wales Police said in a statement that a 22-year-old man had been charged with assault occasioning actual bodily harm after a 35-year-old man had been punched in an alleged "unprovoked" attack.
Rugby Australia (RA) later identified Stannard as the victim of the attack and said they were co-operating with police.
They later said that Stannard had suffered a fractured skull in the attack.
"Stannard remains in St Vincents Hospital in a stable condition, however he has been diagnosed with a fractured skull," RA said. "Rugby Australia will provide a further update on his status as information becomes available."
RA said Stannard and a group of players and team management had been at a fast-food outlet following the dinner for Friend when the alleged attack occurred.
Two players in the squad, including the side's regular captain Lewis Holland, and Friend detained the man shortly afterwards and held him until police arrived, RA said.
Friend was told earlier this month that his contract with the team would not be renewed in July, but RA said they hoped he would remain with the wider organisation.
Australia's women's Olympic gold-medal winning coach Tim Walsh will replace Friend after next month's Commonwealth Games on the Gold Coast.
Stannard had replaced the injured Holland as captain for the tournament.
The men's tournament will be held on the final two days of the April 4-15 Games, with Australia drawn in Pool B with Samoa, Jamaica and England.