"Based on the available information, we do not anticipate major financial claims to arise from this incident, but we continue to assess the situation," Allianz, Europe's largest insurer, said in a statement.
Chinese insurers are also expected to be affected.
"It is still very early to determine the level of insured losses, but the event is likely to be large with initial insured loss estimates of $1-$1.5 billion and a large number of insurance companies affected," analyst Arjan van Veen said on Monday in a note, in which he compiled estimates from a range of Chinese media reports.
Credit Suisse said those affected would be mostly Chinese insurance companies as well as international groups that either insure multi-nationals or provide re-insurance coverage.
Carmakers check damage
As of Monday evening, global automakers had confirmed 4,950 cars were damaged in the blast, with most saying the vehicles were insured but declining to provide additional details.
Volkswagen said that 2,700 of its imported vehicles had been damaged and were mostly "unsellable," according to a spokeswoman.
The number of cars damaged could climb above 10,000 when accounting for all the vehicles in area as automakers struggle to assess the damage as authorities restrict access.
Read MoreScenes from the devastating Tianjin explosion
Hyundai said that 4,000 of its cars were parked in the vicinity, but it couldn't gain access to confirm damages, while Renault's China joint venture has only been able to confirm damages to 1,500 of its 5,000 vehicles in the area.
Renault said the explosion would affect its deliveries in August and September.
Ford, Nissan, Toyota, Daimler and BMW each said their vehicles were affected but they were still assessing damages.
Chinese media said several insurance companies received claims from companies hit by the Tianjin explosions.
"Transport insurers are looking at the damage to containers, warehouses and new cars but also to the port's infrastructure of trains, cranes and rail tracks," Dieter Berg, a marine expert at the world's largest reinsurer, Munich Re, told Reuters.
"In ports, we have a massive concentration of high value (goods) which makes it hard for insurers to make exact risk assessments."
Tianjin's port is China's largest entry point for imported cars, handling roughly 40 percent of cars imported in 2014, according to the official Xinhua news agency.