They were travelling from West Are'are in Malaita province to Marau on Guadalcanal on Wednesday.
The Solomon Star said two boats were doing the crossing together but one, carrying 23 people, failed to make it.
Police said eight people were rescued but one of them has died since.
Police with the help of the Search and Rescue team have been out in the sea to look for the remaining bodies.
The other boat with about 21 people onboard arrived safely.
Photo: Supplied Pacific search and rescue