The volcano, Tinakula, which forms an uninhabited island in the northern Temotu province, roared to life at about 2am yesterday.
Villages on nearby islands have reported heavy ashfall.
The director of the National Disaster Management Office in Honiara, Loti Yates, said a police patrol had been deployed from the provincial capital, Lata.
He said information had been slow to trickle out of the remote area, and it could be some time before the full situation was known.
An aviation warning has been issued for the Santa Cruz area.
Photo: NASA Earth Observatory A satellite image of Tinakula, Solomon Islands, taken in 2012.