"The Rohingya refugee had suffered for a long time with a medical problem" and had previously been sent to Australia for treatment, he added in a statement.
Australia's home affairs department confirmed the death but did not provide further details.
Police say the man's body has been taken to the local hospital and officers are interviewing other refugees who witnessed the incident.
Refugee on Manus Island Behrouz Boochani tweeted that the man had been sent to Australia for medical treatment two years ago, but had not received the help he needed.
"He was suffering for a long time," Mr Boochani tweeted.
Canberra has sent asylum-seekers who try to enter the country by boat to camps on PNG's Manus Island or Nauru in the Pacific for processing, with those found to be refugees barred from resettling in Australia.
The policy is meant to deter people embarking on treacherous sea journeys, but the United Nations and other rights groups have criticised the camps' conditions and long detention periods.
The United Nations High Commissioner for Refugees called for "immediate action" from the Australian government.
The Asylum Seeker Resource Centre said its representatives had met with the Rohingya refugee during a trip to Manus Island last year.
"This man should never have been there in the first place," the ASRC said in a statement.
The 32-year-old man suffered from seizures, according to a press release from the Refugee Action Coalition.
Greens senator Nick McKim also met the man during visits to Manus Island last year.
"Yet another life destroyed by our government's punitive policies," Senator McKim said during a Senate estimates hearing in Canberra on Tuesday.
Human Rights Watch director for Australia, Elaine Pearson, said in a statement: “The news of a sick Rohingya man committing suicide on Manus is sickening. Rohingya refugees clearly cannot return home, given the current situation in Myanmar.
"It’s a travesty that Australia has forced them to spend the last five years playing a waiting game on a remote Pacific island while living in an insecure environment with cutbacks to mental health and other services."
A spokesperson from the Department of Home Affairs told SBS News: "The Department is aware of the death on Manus Island. Further enquiries should be referred to PNG authorities."
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14.