"The worry is that we could see an increase in the frequency and cost of machinery breakdown claims" related to the changeover, senior shipping underwriter Justus Heinrich of Allianz subsidiary AGCS said in a statement.
In October, UN body the International Maritime Organization (IMO) ruled that the maximum sulphur content in ship fuels should drop to 0.5 percent, from up to 3.5 per cent at present.
Ships now face costly refits or fines for non-compliance, with "sniffer drones" set for deployment at major ports to identify polluters, Allianz said.
There are also concerns that traffic might be disrupted if ports do not have enough of the less-polluting fuels in stock, the insurer added.
Turning to annual data on ship safety, Allianz said total losses of major ships were down by 55 per cent in 2018, at 46.
Fewer accidents in dangerous waters in Southeast Asia and a calmer hurricane season limited the toll.
Claims were down by just one percent, at almost 2,700, with the largest number for material damage -- such as an engine failure that led to giant cruise ship MSC Opera's crash into a wharf in Venice on Sunday.