The category four cyclone has been nearly stationary in recent hours and is about 360 kilometres southwest of Rennell.
A gale warning remains in force for Rennell and Bellona, and southern Guadalcanal, and a strong wind warning for Malaita, Western Russell and Makira.
Earlier reports from Rennell and Bellona said up to ten homes had been destroyed and up to 20 damaged.
The disaster management office's director, Loti Yates, says information from many areas is still sketchy.
"There are damages to water supplies in Isabel province because of landslips. There're damages to dwelling houses in southern Guadalacanal, some communities there have faced the full brunt of the strong winds. So it's spread all over six provinces."
Loti Yates says assessment teams will be dispatched to the affected areas as soon as the winds weaken.