She said the incident appeared to be "very significant".
Police can not confirm how many people remain on the island as police and emergency services are unable to access the area due to safety concerns, including the risk of more eruptions and volcanic gasses.
Camera images from the island show people close to the crater rim shortly before the cameras went dark.
In August of that year the New Zealand Defence Force airlifted a 2.4-tonne shipping container onto the island to serve as an emergency shelter in case of an eruption.
He was unclear about the number who remained and were unaccounted for but said the total number of people on the island when it erupted was fewer than 50.
"Everyone that could be taken from the island yesterday were rescued at the time of the evacuation". It last experienced a short-lived eruption in 2016.
Oil prices slip as weak China exports highlight trade war impact
OPEC and allies officially agreed on Friday to cut production by an additional 500,000 barrels per day beginning next month. Elsewhere, sterling traded at $1.3143, not far from a seven-month high of $1.3166 set on Thursday.
Ms Payne said that she had been in contact with her New Zealand counterpart and Australia would be sending more consular assistance today.
Police added that they are "working at pace" to confirm the numbers of people involved.
The country's National Emergency Management Agency said a "volcanic eruption is occurring at White Island and is hazardous in the immediate vicinity of the volcano". "The island is now covered in ash and we are taking expert advice with regards to the conditions to determine when we can safely access the island", he added.
A volcano has erupted on New Zealand's White Island leaving one dead and many unaccounted for.
Ken Gledhill from GeoNet, the country's geological hazard information centre, said: "It's not a particularly big eruption, nearly like a throat-clearing eruption, and that's probably why material won't make it to the mainland".
Most of those on the island were tourists, with many of them from cruise ship Ovation of the Seas.