The cost of a likely multi-year restoration project could itself take a year to become clear, industry experts said.
"It is really going to be up to the French state and benefactors to help to restore and rebuild this," Robert Read, head of art and private client at Lloyd's of London insurer Hiscox told Reuters, adding it could take up to 20 years to restore the cathedral.
"The scaffolding costs are going to be enormous, actually securing the building is going to be enormous. The cost of renovating the (British) Parliament is a similar sort of number," Read said.
The cost of repairs and upgrades to the neo-Gothic fronted parliament building on the banks of the River Thames has been estimated at up to $8 billion.
French President Emmanuel Macron has said France would launch a fundraising campaign to rebuild Notre-Dame, which ranks among the finest examples of French Gothic cathedral architecture.
Several of France's business elite have already pledged money to help, including a 200 million euros ($226 million)donation from Bernard Arnault and 100 million from Francois Pinault, heads of luxury goods groups LVMH and Kering respectively.
"Rebuilding would be very tricky as some of the craft required to rebuild, the stain-making craft would probably have to be relearnt," Hiscox's Read said.
Reinsurer Swiss Re said works of art in buildings such as the cathedral are generally not insured because they are often priceless. Any art works on loan from third parties would, however, be insured, Read added.
While some of the large paintings at Notre-Dame could not be taken down in time, the mayor of Paris, Anne Hidalgo, said at the scene of the fire that a number of the many artworks in the cathedral had been rescued and were being put in safe storage.
Notre-Dame was in the midst of renovations and industry sources said the contractor would have its own liability policy.
"Typically that would be for tens of millions of euros. But effectively that is going to be a drop in the ocean compared to what the actual cost of restoring the cathedral is," Read said.
"If they are deemed to be liable they would be carrying some cover, but it's not unlimited and it's definitely not going to be enough to rebuild the Cathedral."