Beale, who has a lengthy rap sheet, was involved in a verbal altercation with a Wallabies staff member during a flight from Johannesburg to Sao Paolo the day after the side's 28-10 loss to the Springboks in Cape Town.
The management staff member returned to Australia on Tuesday of her own accord, while Wallabies coach Ewen McKenzie on Wednesday said Beale remained available for selection for Saturday's Rugby Championship clash with the Pumas in Mendoza.
An ARU spokesperson said they expected the investigation to be completed by the end of next week.
"The investigation will ensure all parties have an opportunity to present all relevant facts, before any assessment of the alleged incident can be reached," they said.
McKenzie declined to comment on the severity of the allegation or any possible sanctioning, but it's understood the altercation was only verbal.
"We've referred it to the experts," McKenzie said.
"I mean, obviously there's protocols and things in place."
McKenzie refused to divulge whether alcohol was involved, but the Wallabies have a protocol of no drinking on flights and are only allowed to indulge on the night after a test match.
"Matters of integrity, you've actually got to protect the people involved until there is some sort of decision," McKenzie said.
McKenzie admitted he was aware of the incident soon after it happened, but other dramas - including the delayed arrival of the 42-strong touring party's luggage - had slowed the investigation process.
The coach missed Wallabies training in Buenos Aires on Tuesday - their only session so far this week - while dealing with the incident in which he claimed "there were a number of people involved".
Beale's 47-Test career has been dogged by a succession of off-field problems and last year the 25-year-old was forced to undergo counselling and rehabilitation for his struggles with alcohol.
McKenzie, though, said the troubled playmaker shouldn't be hung out to dry.
"Obviously we're aware of the history but you deal with every incident as it comes along," he said.
"And you've got to determine the facts and until we determine that fully, I'm not going to make any more judgment on it."
McKenzie, though, did concede the incident was a major distraction ahead of their final Rugby Championship match.
"These things are time-consuming, so I don't pretend that I enjoy the distraction of it," he said.
"But matters of welfare are critical. Matters of behaviour are critical, too, to team culture.
"So I'm not going to sit here and leave things undone or not attended, so obviously the ARU will take the lead on it but I'll follow it through and make sure things get sorted."
