It is understood the vessel MV Taimareho was carrying passengers from the capital Honiara to West Are Are in Malaita Province last night when it encountered bad conditions.
The Solomon Islands Maritime Rescue Coordination Centre says it only received word of the stricken ship's ordeal late this morning, and its officers are scrambling to launch a rescue operation.
According to the cente, the vessel encountered very rough seas and strong winds whipped up by Cyclone Harold between 2am and 3am this morning - a number of passengers were washed overboard.
An official headcount is still being conducted but it is feared as many as 60 people could be missing.
A police patrol boat is expected to be dispatched to the area today to assist with rescue efforts.
Australia donates emergency funds to Solomons amid cyclone
Australia has donated more than $US60,000 in immediate emergency funds to the Solomon Islands to assist with its response to damage being caused by Cyclone Harold.
The category one cyclone was about 245 kilometres southwest of Honiara this morning, moving east-southeast at 14km/h.
Already locals are posting pictures on social media of heavy flooding and fallen trees damaging buildings.
The most pressing concern is for people on the islands of Rennell and Bellona which Cyclone Harold was forecast to be passing by in the last few hours.
In announcing its emergency assistance, the Australian High Commission in Honiara said Australia stood ready to assist further as the extent of the damage became known.
The High Commission said Australia's thoughts and prayers were with the people of Solomon Islands.
Meanwhile, the Australian Bureau of Meteorology said in the longer term the weather system was expected to continue moving towards the southeast.
It may affect Vanuatu late in the weekend or early next week as a severe tropical cyclone.
Photo Australian HC in Solomons Caption: Flooding on the Kumkum Highway in Honiara