Australia beat Argentina 14-13 in Perth on Saturday and the squad, including 23-year-old O'Connor, were given a week off before this weekend's departure to South Africa for a match in Cape Town on September 28.
A statement from the Australian Federal Police read: "The AFP can confirm it spoke to a 23-year-old man at Perth International Airport in the early hours of the 15th of September (Sunday)."
"It is alleged the man was intoxicated. The airline said the man was booked to travel with made a decision not to allow him to board the aircraft. The AFP subsequently escorted the man from the terminal."
O'Connor, who played fly-half for Australia in the British and Irish Lions series earlier this year before moving back to the wing for the Rugby Championship, has won 44 caps for his country since his debut in 2008.
"Earlier this week, Australian Rugby Union was made aware of an alleged incident involving James O'Connor at Perth International Airport in the early hours of Sunday 15 September," said an Australian Rugby Union statement.
"While ARU had not received any formal notification, complaints or reports from police, airline or security officials, ARU began an investigation into the alleged incident.
"The investigation is ongoing."
While prodigiously talented, O'Connor does not have a flawless disciplinary record off the pitch and has been involved in a string of incidents while representing his country.
Most notably, he missed the official launch of Australia's 2011 World Cup campaign at Sydney airport after sleeping in. He was also photographed at a fast food restaurant at 4 a.m. with fellow Wallabies back Kurtley Beale during the Lions series.
O'Connor, who is without a Super Rugby team after being dumped by the Melbourne Rebels, conceded after the Lions series that he had some work to do to regain the trust of some of his team-mates.
"I don't play rugby to be talked about off the field," he said at the time.
"I'm playing rugby because I love it and that's what I want to be doing, playing for my country. At the moment I'm doing the hard yards and I'm trying to get involved and earn myself into the team."
"It's not hard to do, it's just putting the team first.
"There's definitely things that I already have changed and am in the process of doing, personal things."