"I predict one day Amazon will fail. Amazon will go bankrupt," the billionaire said, replying to an employee who asked him about the company's future, in relation to the bankruptcies of big US retailers such as Sears.
"If you look at large companies, their lifespans tend to be 30-plus years, not a hundred-plus years."
A recording of the meeting was heard by CNBC.
In it, Mr Bezos added that the way for Amazon to stay successful is for staff to "obsess" over customers.
"If we start to focus on ourselves, instead of focusing on our customers, that will be the beginning of the end," he said.
His comments accompany a wave of major success for Amazon, even as the company comes under heightened scrutiny.
Both Amazon and local authorities in New York attracted heavy criticism after the company revealed that it would receive around $1.5bn in incentives, based on job creation targets, in Long Island City, and $573m in Arlington.
Two of the sites chosen for Amazon's new campus in the city were originally intended for affordable housing and the decision is now likely to cost the city around 1,500 residential units intended for low and middle-income New Yorkers, according to Politico.
The announcement followed an extensive "beauty pageant" process, which saw 238 competing proposals submitted from locations across the US.
Amazon, which now employs more than 600,000 people worldwide, said salaries at its two new bases would average more than $150,000, with hiring set to start next year.
Staff at the company told CNBC that employees are worried about the impact of government regulation and potential antitrust violations.
In September the EU's antitrust watchdog launched a preliminary investigation which is examining how Amazon uses data from third-party merchants.
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