At least 114 people died and some 700 were injured in last week's blast.
Residents are demanding compensation and firms have seen their assets damaged and production disrupted.
Thousands had to evacuate their homes after toxic chemicals were detected in the air following the blasts at the world's tenth-busiest port.
Based on official Chinese media reports, bank Credit Suisse estimates the losses could amount to $1-1.5bn (Â£640-957m).
Ratings agency Fitch though warned the bill could be much higher.
"Claims from the blasts are likely to undermine the financial performance of some regional players and those property and casualty insurers with high risk accumulation in the affected areas," Fitch said.
Local Chinese insurers are expected to bear the brunt of the costs.
Investigations into the cause of the blast are still ongoing and the damage is still being assessed.
Aside from the actual damage, a number of factories near the blast site have halted operations leading to losses that could also be compensated by insurers.
Japanese car maker Toyota said more than half its China production capacity would be affected at least through Wednesday.
The company said it had suspended all three production lines at its plant near Tianjin, which can produce 530,000 vehicles a year.
The car maker also said it could divert shipments to the ports of Shanghai and Dalian in response to the severe logistical problems resulting from the Tianjin damage.
Thousands of imported Volkswagen, Toyota, Hyundai and Renault cars, parked near the blast site were damaged in the explosion.
Operations of electronics company Panasonic, logistics firm Singamas Container Holdings and of US maker of agricultural machinery Deere & Co. have also been disrupted.
More on the deadly Tianjin blast:
China explosions: Doubts raised over chemical licences
Potent chemical mix behind blasts
What we know about explosions
The questions being asked by Chinese citizens
'Hero' firefighters hailed
'Like the end of the world': Residents' stories
Insurance claims after the deadly Tianjin blast could far exceed official estimates, Fitch ratings agency has warned.