The organization told "Good Morning America" that shoppers should be aware of bogus calls that claim to be from Amazon's "Fraud Department" and instruct victims to "press one" to speak to an executive.
The calls sometimes show up as legitimate numbers from the BBB and other credible organizations
"Once you press one, you open yourselves up to whatever it is they're wanting from you, your personal information, your Social Security, your bank, your driver's license," said Lori Wilson, the CEO of the BBB's Oakland office.
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The BBB said the scammers tell victims that they have problems with their Amazon accounts, like a lost package or a declined credit card payment.
They then ask for personal information like an Amazon account login, credit card number or date of birth.
"They're targeting anybody with a phone. Whether it's a business or whether it's a somebody who doesn't own their own company, you're a target," Wilson said.
Amazon told "GMA" that the company works hard to protect against "bad actors that fraudulently use our brand."
The company said customers should be skeptical of unsolicited calls and avoid making payments outside the Amazon website.
Consumers should also ignore demands for urgent action, as scammers want victims to react fast without thinking.