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

Patterdale terrier Taz became trapped beneath a concrete terrace at Bath City FC on Thursday night.
Crews from Bath Fire Station had to remove part of the stand at the Twerton Park ground to get to the dog.
A spokesman for Avon Fire and Rescue said: "Once crews reached the terrier they found he was still pinched between the bottom of the stand and soil and rubble below."
The spokesman added: "Firefighters were able to dig out the ground around Taz before pulling him to safety through the gap.
"Once free, he was reunited, unhurt, with his extremely grateful owners."
Bath City have been approached for comment.

Researchers from the Eötvös Loránd University in Hungary have found that dogs can recognise certain words and even tell the difference between how the words are being said.
They found that the animals can tell if the words are positive like or negative and can understand the tone of voice used to say them.
They trained a group of dogs to lie really still in an MRI scanner, which is a bit like an x-ray for your brain.
It told scientists how the dog reacted to different things by measuring which part of their brain was used in response the test.
The scientists played the dogs recordings of words said in a happy or a normal tone of voice to see how they would react.
By looking at the MRI scans the scientists found that the dogs recognised certain words, and could tell the difference between how the words were being said, in the same way that humans do.
When the dog was played a recording of a positive message said in a happy voice the scans showed the dogs processed that information in the part of the brain that deals with rewards and happy feelings.
One of the researchers Attila Andics explained that: "This shows… that dogs not only separate what we say from how we say it, but also that they can combine the two for a correct interpretation of what those words really meant."
Insurance claims after the deadly Tianjin blast could far exceed official estimates, Fitch ratings agency has warned.
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A dog has been rescued after getting stuck under a football stand.
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Ever wondered if your dog can REALLY understand what you are saying?