"They're not making money in retail, and they're putting retailers out of business," Simon told CNBC.
According to a recent analysis by One Click Retail, Amazon accounts for 4 percent of U.S. retail and captures 44 percent of online retail sales.
Simon told CNBC the e-commerce giant has operated its retail segment at a loss for decades, subsidizing the retail portion of its business with profits from other areas, such as web services.
"It's anti-competitive, it's predatory, and it's not right," said Simon.
"It's not going to hurt the big ones," said Simon, who served as president and chief executive officer of Walmart U.S. from 2010 to 2014. "Walmart can adjust. It'll be there. Costco will continue to thrive."
"That's because Amazon sells below cost and continues to do that," said Simon, who serves on the board of directors for Darden Restaurants. "It's destroying jobs, and it's destroying value in the sector," he said on "Closing Bell" on Thursday.
Amazon has disrupted the retail sector, forcing companies — both big and small — to adjust. That includes Walmart, a brick and mortar powerhouse that observers see as one of Amazon's biggest competitors in the retail space.
Amazon posted its largest ever profit in the fourth quarter of 2017, reaping nearly $2 billion. During that time frame, sales rose 38 percent to $60.5 billion, beating Wall Street's estimates.
In response to Simon's critique, an Amazon representative told CNBC that while the company's activities are primarily retail-based, it does not break out specifics. For that reason, he added that Simon has no real basis to say the company is operating at a retail loss.
"Unlike others, they pay little or no taxes to state & local governments, use our Postal System as their Delivery Boy (causing tremendous loss to the U.S.), and are putting many thousands of retailers out of business!" Trump posted on Twitter last week.
A 1992 Supreme Court ruling said states couldn't collect sales taxes gathered by mail-order catalog companies unless the businesses had a physical presence in a state. But some states say online retailers should be required to collect sales tax, even without a physical presence.
"It came down to a Supreme Court decision that came down three years before Jeff [Bezos] shipped his first book," Gerald Storch told CNBC on "Closing Bell."
Storch, former vice chairman of Target, who founded Target.com in the late 1990s, and former CEO of Toys R Us, called the ruling "an antiquated decision."
"If you read that Supreme Court decision … it was based on all kinds of things that simply don't apply anymore," said Storch, who worked with Amazon and Jeff Bezos in 2001. "At that point, e-commerce was nothing; it was zero. Now it's taken over the whole economy."
Storch pointed out that half of all online product searches begin and end on Amazon, and said the playing field in retail should be more level, something it has not been in the past.
"Amazon is a lot more powerful than people realize," he said.