Victoria Police chief commissioner Graham Ashton said the alleged offender purchased his ticket after being released from the facility and then boarded the plane.
The jet was forced to return to Melbourne after the passenger allegedly tried to enter the cockpit, claiming to have explosives.
Brave passengers tackled the man about 20 minutes into flight MH128 that departed Melbourne for Kuala Lumpur at 11.11pm.
The Airbus A330 landed back at Melbourne Airport without incident.
Passengers say they were then forced to endure a wait of over an hour until police boarded the plane.
Mr Ashton said the man, a Sri Lankan national, was being interviewed by police and was expected to front court later today.
He said the man was had been a voluntary patient at the psychiatric facility.
The Chief Commissioner said while he understood passengers were distressed about enduring a long wait on the tarmac he believes the time gaps were not problematic.
He said the delay in getting passengers off plane was due to concerns there may have been an accomplice on board or a second “device”.
Mr Ashton said the incident was initially treated as a terror matter, but it has since been established it was not.
Man dragged off flight by police in Melbourne after threatening to 'blow up the plane'
Former Melbourne AFL footballer Andrew Leoncelli, who was on the flight, told how he tried to stop the man.
“We literally took off, 10 minutes into the take off, and I was sitting in business class 4A seat, and I could hear this idiot saying that he wanted to go in and see the pilot,” he told 3AW.
“The staff were saying ‘sit back down sir, sit back down sir’.
“He goes, ‘no, I’m not going to sit back down – I’m going to blow the plane up’.”
Mr Leoncelli said once they landed safely, passengers were kept on the plane on the tarmac for more than an hour before police boarded.
“We sat on the tarmac for an hour and 20 minutes waiting for the police to come and we were praying that it wasn’t a bomb,” he said.
Passengers Stan and Pam Young, flying on to London, were angry they were not evacuated sooner.
“If there was a bomb on that plane we should have been communicated (to) ... instead, we sat there for another hour and a half.
“There was no communication.
“They literally left us waiting and wondering.”
Police would not go into detail about the moments after the plane landed, citing “operational matters”.
“I’m not going to go into specifics of times at this point,” Victoria Police Superintendent Tony Langdon said.
“As I was saying, these are operational matters.”
Australian Federal Police Superintendent Martin Goode said: “The safety of passengers is paramount, and we need to consider a number of options, and Victoria Police was handling that side of things, in discussion with us, and we needed to make sure that all contingencies were covered.”
Victoria Police say a 25-year-old Australian citizen from Dandenong in Melbourne’s southeast is in custody.