Sir Michael served three terms as prime minister over 17 years, and he was the first post-colonial leader of the country in 1975.
He and wife Lady Veronica had been preparing this week to go overseas for treatment.
A family member said: "It is with sadness that I advise, on behalf of the Somare family, the serious illness pancreatic cancer that has befallen our father, Sir Michael, it is at a critical stage and we as a family, along with his medical teams, are giving him the utmost care that he deserves.
"After comprehensive consultation to ensure all clinical opportunities were exhausted in every jurisdiction with the competencies able to treat the critical stage of this form of cancer, the family, in consultation with the Grand Chief and Lady Veronica, have settled with offering the best palliative care and nutritional and dietary care in PNG.
"Due to many inquiries, we thought it best to be forthright so the public knows the exact extent of this terrible illness.
"We thank the many Papua New Guineans who have sent in their well wishes and prayers for the health and wellbeing of Sir Michael and Lady Veronica."