The eruption has covered the Pacific islands in ash, cut power and severed communications.
Up to 80,000 people there could be affected, the International Federation of Red Cross and Red Crescent Societies (IFRC) told the BBC.
New Zealand Prime Minister Jacinda Ardern said the tsunami had wreaked "significant damage".
No deaths have been reported so far.
Information remains scarce, however, and New Zealand and Australia are sending surveillance flights to assess the extent of the damage.