RNZ reports disaster authorities said around 200 buildings had been destroyed or damaged in the provinces of Makira & Ulawa, Malaita and Guadalcanal.
Among them were 11 schools and a medical clinic.
Some dwellings were also hit by waves generated by Friday's 7-point-8 magnitude quake and Saturday's 6-point-9 aftershock.
The country director for World Vision Solomon Islands Janes Ginting said the tremors had left communities very nervous.
"What happened after the earthquake, you know, some people returned to their home and there's another aftershock. Of course they went to higher ground and some of them went to the clinic and after the aftershock they went back to higher ground so there's still a lot of anxiety among the people there after the shocks and tremors."
Emergency response teams arrived in Makira and Ulawa Province on Monday and were expected to reach affected communities today.
The province was the closest to the epicentre of the quakes.