Immigration Minister Scott Morrison said 77 asylum seekers were injured on the second night of violence at the center on Manus Island, part of Papua New Guinea.
He called the death of the unnamed asylum seeker, who died Monday on the way to Lorengau Hospital on Manus Island, a ''great tragedy."
An investigation will look into what caused the riots, including who shot the man, Morrison said.
"That's a matter for a police investigation and I don't have any further information," he said.
A report by the Sydney Morning Herald quoted Morrison saying there were two shots fired by PNG police as they battled several hundred asylum seekers who had breached a perimeter fence.
Morrison denied reports that it was police and locals armed with machetes who broke down the fence, entered the center and attacked detainees.
"That's not how the fence went down," he said.
Security outside the center, not in it, is handled by PNG police, he said.
The second night of rioting came after police and staff from G4S -- the global private security firm that runs Manus -- quelled disturbances Sunday night and captured 35 escapees.
Monday night's rioting was more severe, starting at about 6 p.m. and lasting until 2 p.m..
The clashes between detainees and police are another blow for Australia's controversial policy of holding asylum seekers in offshore centers.
The asylum seekers, most from Afghanistan, Sri Lanka, Iraq and Iran, head for a new life in Australia after paying people traffickers often thousands of dollars for passage in overcrowded boats.
Australia signed an agreement with Papua New Guinea in 2012 to re-open the center on Manus, a rugged jungle-covered island measuring off Papua's northern coast.
Australia also reopened a center on Nauru, a small island republic in the South Pacific with a population of about 9,000.
The policy is not to allow asylum seekers into mainland Australia but resettle them in third countries.
Disturbances on Sunday night reportedly happened after immigration officials told detainees they would not be resettled in Australia.
Amnesty International published a report on Manus in December, claiming conditions for the 1,300 detainees were "shameful."
Amnesty said asylum seekers are being held in a "prison-like regime," in extremely cramped compounds in stifling heat with insufficient water and medical treatment.
Conflicting accounts about Monday's events have surfaced, claiming PNG police entered the Manus center to attack detainees, the Herald reported.
An asylum seeker from Lebanon wrote in a Facebook message that the violence had started again.
''Tonight police and G4S attack us again. Many peoples in the yard. Injure please we need one to help us. May be till morning they will kill us," the detainee wrote.
The Herald reported one man received a distressed call from his brother, a detainee in Manus who said he was covered in blood from stones being thrown at him and he had to run to save his life.
The Herald also reported G4S said claims of ''internal attacks'' within the center were unfounded.
In a statement, G4S said it had removed from the compound all ''non-essential'' staff as well as asylum seekers who weren't involved in rioting.
The G4S statement also said asylum seekers were injured after they had broken out of the center.
Teacher apologizes for showing sexual image of herself in class
Susan Sarandon 'very excited' about daughter's pregnancy