Whole Foods Markets (WFM) stole more customers from Walmart Stores Inc. (WMT)  than any of its competitors after it cut prices following its Amazon (AMZN)  takeover, according to fresh data published Tuesday, but the upscale retailer is still relying on wealthier shoppers.

Thasos Group, a research firm that uses mobile phone location data, said Whole Foods's foot traffic increased by 17% in the week that began on August 28, the day the $13.7 billion Amazon deal closed, when compared to the same period last year. That slowed to around 4% by September 16, Thasos said, but remained "elevated" compared to the weeks prior to the takeover.

"Whole Foods new customers overwhelmingly belonged to the same upper income demographic as the company's traditional customer base," Thasos said. "Defecting customers in the week of the price cuts came from the wealthiest segment of each competing store's customer base."

Around a third of that new traffic, Thasos estimates, came from Wal-Mart and Sam's Club's regular customers over the first week of the price cuts, with Kroger Co. (KR) (16%) Costco Wholesale (COST) (15%) and Target Corp. (TGT) (11%). Looking at the changes in traffic from Whole Food's direct competitors, however, shows that Trader Joe's, Sprouts Farmers Market Inc. (SFM) and Target saw the largest percentage of customer defections, Thasos said. 

"We see its acquisition of Whole Foods as greatly enhancing its distribution network and making this massively under-penetrated opportunity, as is evident by the nearly $900bn US grocery market being only 3% penetrated, much more addressable," Wells Fargo Securities LLC analyst Ken Sena wrote in a client last week.

Amazon's Whole Foods acquisition gives Amazon an instant foothold in the grocery market, one it's long struggled to break into with its food e-commerce programs, Prime Pantry and Amazon Fresh, TheStreet's Laura Berman wrote last week, but noted that price is the main reason many avoid shopping there.

Morgan Stanley analysts found that 13 million households shop at Wholefoods, compared to 24 million at Kroger,  6 million at Sprouts and 3 million at Smart & Final Stores Inc. (SFS) . 

Watch More with TheStreet:

More from Stocks

Constellation Brands COO Discusses Investing in Canopy Growth

Constellation Brands COO Discusses Investing in Canopy Growth

Jim Cramer: The Move Out of Regional Banks Is Fed-Fueled

Jim Cramer: The Move Out of Regional Banks Is Fed-Fueled

Facebook, Fed Minutes, AmEx, PayPal and Endocyte - 5 Things You Must Know

Facebook, Fed Minutes, AmEx, PayPal and Endocyte - 5 Things You Must Know

A Value Play in MSC Industrial

A Value Play in MSC Industrial

Jim Cramer Dives Into Cannabis and IBM Earnings

Jim Cramer Dives Into Cannabis and IBM Earnings