Hackett's father Nev said the 36-year-old had been detained over "mental health issues" but refused to comment further, according to the Courier Mail.
The swimmer, who won the men's 1500 metres freestyle at the Sydney Olympics in 2000 and at Athens in 2004, remains in custody.
The 10-time world championship gold medallist has struggled in his personal life in recent years, after retiring from the sport in 2008, making a brief and unsuccessful comeback attempt in 2015.
In April last year, Hackett apologised after being accused of "forcefully" groping a passenger and "tweaking" his nipple on an interstate flight following a dispute over a seat being reclined too far.
Hackett phoned his alleged victim to apologise for his actions on the flight from Adelaide to Melbourne. He pledged to donate a sum of money to a charity of the man's choice.
"I seriously and genuinely regret my poor behaviour," he said in a statement. "I have stuffed up more than once and am working on these issues."
It came a couple of years after the former Olympic hero spent time in a US rehab clinic where he was treated for a sleeping pill addiction after photos emerged of him looking lost with a singlet wrapped around his waist as a pair of shorts.
Before that there were two other high profile controversies. In 2011 he trashed the Melbourne apartment he shared with then-wife Candice Alley, who was home with their twin sons.
Eight police cars were called to the luxury apartment after a distressed 000 was made to police.
Pictures emerged of the damage caused in the apartment - which included some of the items his wife most cherished like her piano, a dresser and framed photographs. A bedroom door was also destroyed, as were some of the children's toys. The couple later said they were dealing with some "private issues".
Months later, Hackett had an alcohol-fuelled night at Crown Casino during and after the Logie Awards in April 2012, where he was asked to leave a Channel 9 party and fell asleep in a stairwell.
At about 3am, the Olympian was approached by bouncers at a nightclub in the casino complex and told he should "call it a night". Hackett is said to have fully co-operated with staff and left promptly without an escort.
The following morning, Channel 9's Today aired footage of a sweaty Hackett at the party struggling to form a sentence. Asked by a reporter for his favourite song, Hackett stumbles: "I don't know my favourite song 'cos there's are so many favourite songs. 'Cos if I could name one I would."
He and Alley split a month later and he was dumped from his ambassador role at the Alannah and Madeline Foundation which aims to protect children from violence.
