Hackett didn't specify where he was flying to, but said it was part of a wider treatment plan.
"I said that was part of my treatment plan, among many other things," he said. I'll be in a few different locations and hopefully come back with a big smile on my face."
The latest episode is one of several to dog Hackett, but the 36-year-old was confident this was another challenge he could overcome.
"We all go through our ups and downs in life and you always get back on top eventually," he said.
Hackett was arrested on February 16 and taken to Southport watch-house, before being released. No charges were laid.
Older brother Craig said at the time that Grant needed help to deal with his problems.
"To see someone who was so dominant and had the world at his feet, to now really we don't know what's going to happen. It doesn't look encouraging," he said.
"If he gets the right type of treatment, and that's what we're really counting on, maybe, just maybe, he might be able to claw himself out of it.
"This is not Grant Hackett. I don't know this person, my mum and dad don't know this person.
"He's there in body, but he's not there in mind, soul or spirit. Poor Mum and Dad have tried to look after him so much.
"If there's anyone out there that can help him, we're all for it."
Last April, Hackett apologised, after an incident with a fellow passenger on a flight that landed at Melbourne. He phoned the alleged victim to apologise for the incident.
"I seriously and genuinely regret my poor behaviour," he said, in a statement at the time.
"I have stuffed up more than once and am working on these issues.
"It is embarrassing to hear and read the consequences of my actions. I apologise unreservedly to the gentleman on the flight.
"I am trying to make direct contact with him personally. I know I have to front the media and discuss my actions in a more appropriate and accountable way.
"I just have to sort a few things first, so I can be as frank and open as I need to be. I apologise for the inconvenience."
Hackett was questioned by police over the incident, but not charged.
In 2011, he was at the centre of the police investigation, after losing his young son at Crown Casino in Melbourne.
Also in 2011, police were called to the apartment he shared with ex-wife Candice Alley following an incident.
Early last year, Hackett fell short in his Olympic comeback bid.