At least 300 litres of diesel is believed to be on board and a small amount has washed up on shore.
Staff are assessing how it can be removed and while the risk of contamination is minimal, people should be cautious if harvesting shellfish nearby and not eat anything with a diesel smell, said council senior regional hazards advisor Dave Lovatt.
Three marine farms operating in the harbour have been contacted by the council.
Staff are also liaising with the vessel's owner on a salvage plan.
It is likely the boat will remain in the water until at least next week, with the first priority extracting the remaining fuel," Mr Lovatt said.