Global commercial insurance premiums rose 11 percent on average in the first quarter, according to insurance broker Marsh, which said the war was putting upward pressure on rates, reports Reuters.
But the overall figure masks sharper moves in some sectors, and only covers the first five weeks following the invasion.
War is typically excluded from mainstream insurance policies. Customers buy an extra war cover on top.
Garrett Hanrahan, global head of aviation at Marsh, said aviation war insurance was no longer available for Ukraine, Russia and Belarus as a result of the conflict.
For the rest of the world, aviation war cover has doubled, as insurers try to recoup some of their losses, he said.
"The hull war market is beginning to reflate itself through rate rises."
The conflict, which Russia calls a "special military operation", could lead to insurance losses of $16 billion-$35 billion in "specialty" insurance classes such as aviation, marine, trade credit, political risk and cyber, S&P Global said in a report.
Aviation insurance claims alone could total $15 billion, S&P Global said, with hundreds of leased planes stranded in Russia as a result of western sanctions and Russian countermeasures.
One aircraft lessor described recent rate increases on its insurance as "not a pretty sight".
Some aircraft lessors - a particularly exposed sector of the market because their planes are stuck in Russia - were now having to pay 10 times their original premium, one underwriter said, while another said insurers could "name their price" to lessors.
In ship insurance, policyholders pay an additional "breach" premium when a ship enters particularly dangerous waters, locations which are updated by the Lloyd's market.
For the area around Russian and Ukrainian waters in the Black Sea and Sea of Avov, this has increased multiple times, three insurance sources said, to around 5 percent of the value of the ship, from 0.025 percent before the invasion, amounting to millions of dollars for a seven-day policy.
Each time a ship goes into those waters, it has to pay that extra premium.
Rates for ships going into other Russian waters have also risen by at least 50 percent after the Lloyd's market classified all Russian ports as high risk, two of the sources said.
Because of the dangers, some marine insurers have also stopped providing cover for the region.