Insurance for boats sailing into Lebanese and Israeli ports is also likely to be affected as governments seek to evacuate their expatriates in Lebanon.
The London market has begun to price cover in preparation for vessels entering the region.
A marine spokesman for Lloyd's broker, Aon, said: "Lebanon is an excluded area for hull war risks, so evacuation vessels will be charged an additional premium. As a result of the conflict there has been a sudden hike in rates from 0.1% last week to 0.25% today."
Tim Turner, a marine hull underwriter at Beazley, added: "The weekly breach rates for vessels calling either in Lebanon or Israel, have dramatically increased in the last week and move on a daily basis as events unfold."
Israeli warplanes are targeting Hezbollah fighters, who have captured two of its soldiers.
The country has continued its air raids over southern Beirut and others parts of Lebanon.
Meanwhile Hezbollah has continued to fire rockets into northern Israel.