Hooper trained with the team this week and was selected to play on Saturday against Argentina, but informed management he wished to withdraw from the fixture and return to Australia.
"(There was) nothing that was evident to us, how he trained and how he contributed around the team, around leadership was excellent but clearly he's been struggling a bit and masking that pretty well," Rennie told reporters.
"But it came to a head last night and he was brave enough to call Sharon (Flahive, Wallabies team doctor) and have a chat with her and then involved (team manager) Chris Webb and myself to get an understanding of where he is at.
"The concern is all around his welfare and it was an easy decision to let him go home where he'll get plenty of support around him."
Prop James Slipper will lead the side in Hooper’s absence, while his place in the team at flank has been taken by Fraser McReight.
"It's not uncommon in life is it?" Rennie said of Hooper's issues. "(Rugby's) a cross-section of society. Often men will say bugger all and suffer in silence.
"It took a lot of courage from him to address the group, so a huge amount of respect from everyone and respect that we want to get him home and get as much support around him as we can."
"Michael’s one of the most professional and impressive men I’ve coached. I know this has been a difficult decision for him," Wallabies coach Dave Rennie said.
Hooper will return to Australia accompanied by his New South Wales Waratahs team mate Dave Porecki, who was already ruled out of both tests against Argentina after sustaining a head injury in training.
"While this decision did not come easily I know it is the right one for me and the team at this point in time," Hooper said in a media release from Rugby Australia.
"My whole career I’ve looked to put the team first and I don’t feel I am able to fulfil my responsibilities at the moment in my current mindset."
There has been no indication from Hooper whether his decision to step away from the game is a temporary one, or will be an extended break.
"We're not putting any time frames on it," Rennie said when asked how long Hooper would be sidelined.
"Obviously he's felt he's been able to suppress things over the past handful of weeks so we certainly weren't aware of anything," Rennie added.
Prop James Slipper, who has played 110 times for Australia, will captain the Wallabies in Hooper's absence while Fraser McReight takes over at the number
The 30-year-old made his test debut in 2012 and has played 121 times for the Wallabies. Last year he passed George Gregan's record for the most tests as captain. Some indifferent form for the team, including last year's autumn internationals and last month's 2-1 home series loss to England, put Hooper's captaincy in the spotlight, but he has as yet given no specific explanation of his mindset issues.
With a little over a year to go until the Rugby World Cup in France, Hooper's future with the team now hangs in the balance and while Rugby Australia will support him, they will also be keen to hear his plans. McReight is a solid replacement in the short-term, having been in good form for Queensland Reds and a surprise omission from the England series.
Australia take on Argentina in the Rugby Championship on August 6th
