The Campaign, a coalition of NGOs, organised the nuclear weapons ban treaty adopted in July by 122 states, including six pacific countries, in the UN General Assembly.
Dr Griffen, a long-time anti-nuclear advocate, says it'd be significant if all 12 Pacific island states ratified the treaty.
"That would be quite a high percentage of the fifty that we need. And we have I think a vested historical and moral and health interest in this treaty, because there are two sections of it, on victims assistance and environmental remediation, which are directly relevant to the Pacific," said Dr Vanessa Griffen.
Dr Griffen says the Nobel award is timely given the treaty and the current threat of nuclear war.
North Korea threat
The level of threat over the North Korean nuclear programme, was also mentioned this morning in Oslo by the Campaign's executive director, Beatrice Fihn, in the Nobel Prize acceptance speech.
Animosity between US President Donald Trump and the North Korean leader Kim Jong-un had created a risk of global nuclear annihilation greater than during the Cold War.
Ms Fihn said that it showed how widespread destruction which would affect the whole world was just one "tantrum away".
"We have a choice, the end of nuclear weapons or the end of us," said Ms Fihn.
While 122 nations signed the treaty, at least fifty would to have the treaty ratified in their own country for it to enter into force. The six Pacific Island countries that signed the treaty at the UN are Fiji, Kiribati, Palau, Samoa, Tuvalu and Vanuatu.
According to Dr Griffen, the direct experience of being affected by nuclear testing in the Pacific Islands region remained important.
he said because Pacific people understood the effects of radioactivity, particularly in states such as Marshall Islands and the French Pacific, their commitment to the anti-nuclear treaty was significant.
"The Pacific states have been really great, not just in the immediate adoption of the treaty, but all the years before of... having a resolution to say we must negotiate for a treaty, attending the humanitarian conferences that preceded the General Assembly resolution that produced the Treaty process."
Of the bigger countries in the wider South Pacific region, Indonesia, New Zealand and Chile signed the treaty. However Australia voted against the resolution, along with nuclear weapon-bearing states like the US, Israel, Russia, France and the United Kingdom.