The man died of head injuries on the way to hospital, Australian Immigration Minister Scott Morrison said.
Thirteen people suffered serious injuries, including two who are being transferred to Australia for treatment, one with a gunshot wound.
He said the injuries occurred outside the camp, after the men broke out.
Australia sends asylum seekers arriving by boat for detention and processing in offshore camps in Papua New Guinea and the Pacific territory of Nauru.
Conditions in these camps have been strongly criticized by UN agencies and rights groups.
The violence took place late on Monday night.
The violence comes after some of the detainees briefly escaped from the detention centre on Sunday.
In recent months Australia has taken a very tough stance in a bid to halt the flow of asylum seekers, who arrive by boat via Indonesia.
Manus Island is one of two offshore processing camps in which asylum seekers are detained.
Australia has also initiated a policy – aimed as a deterrent – whereby those people found to be genuine refugees will be settled in Papua New Guinea rather than Australia.
Sunday’s break-out is reported to have taken place after detainees were told that they would not be resettled in Australia.
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