Walmart "went out head to head, knuckle to knuckle and won market share in retail by executing a business model that customers wanted," said Simon, in an interview with CNBC's "Squawk Box."
By contrast, Amazon is doing something similar to Walmart but also "losing money at it," Simon said. "They're gaining traction and profitability by other business activities that have nothing to do with retail," including Amazon Web Services and advertising.
Amazon did not immediately respond to CNBC's request for comment.
Amazon, with a market cap of more than $782 billion, has seen its shares rise more than 61 percent over the last 12 months as it continues to take business from older, big-box rivals.
The company saw growth in both its cloud service and ad business in its latest quarter, bringing in $5.44 billion and $2.03 billion in sales, respectively.
Amazon's subscription revenue also saw a jump, up 60 percent in the first quarter to $3.1 billion.
Walmart has been making moves to take a piece of the fast-growing online market.
Earlier this month, Walmart agreed to pay about $16 billion for a 77 percent stake in Flipkart, India's largest e-commerce company. India is seen as an important retail battleground.
Simon, speaking ahead of both Walmart's and Amazon's shareholder meetings this week, wondered about Walmart's "expensive" trip into e-commerce but at the same time applauded the company's commitment to online.