The Tinakula volcano in the country's easternmost Temotu Province began erupting on Saturday spewing ash over the Reef Islands in the Santa Cruz group.
A volunteer disaster worker in the provincial capital Lata, Jones Harara, said the volcano continued to spew ash and lava.
Mr Harara said people in Lata could hear the eruptions 20 kilometres away.
He said those directly affected by the ashfall were in urgent need of relief support.
"They use coconut only. Maybe it will take [last] a couple of days before they look for some relief supplies for them," said Mr Harara.
"I think we should call on the government. They need something to support them now."
An aviation warning has been issued for the Santa Cruz Islands and national disaster authorities have urged local people to stay indoors and protect their water supplies.
Photo: NASA Earth Observatory A satellite image of Tinakula, Solomon Islands, taken in 2012.