A sustained fall on stock markets would deny insurers vital income from investments, analysts fear.
“This year is crucial for insurance companies because they can't rely on investment returns to shore up underwriting losses,” said one analyst at a UK bank.
“The point is that equity markets in general aren't going to react positively to this.”
He predicted that the major reinsurers would survive but for less well-established companies, the effects of Tuesday's attacks could prove fatal.
“It's probably the smaller players that will suffer most,” he said.
He said larger companies could eventually see their positions strengthened if the number of their competitors falls.
He believed that of the major reinsurers, Munich Re were the best placed to ride out the storm.
“The balance sheets of Zurich Re and Swiss Re aren't as strong as Munich Re.
“Munich Re are better placed because they've got a stronger capital base, in my opinion. I would say Zurich is worst off and Swiss is slightly better.”
In the case of Zurich Re, Mr Shaw warned Tuesday's events could endanger the company's strategy into the medium term.
He said Swiss Re would gain from its business in property and casualty insurance but he feared its long term strategy could be undermined.
He said: “What happens if we have another event like this in a month's time?
“It's going to take a long time to unravel this. Claims will keep coming back to haunt th
