But a closer look at a broader set of products suggest the discounts are still modest, according to Gordon Haskett analyst Charles Grom.
Grom wrote in a note published Tuesday that the average price of 114 products he tracked from last week declined by only 1.2% week-over-week as of Monday. The deepest discounts came from the dairy/yogurt category (5.6%), but 78% of the 114 products he tracked didn't see any discounts, meaning it remains to be seen how far Amazon will go with its price cutting.
Grom's analysis may be limited because it comes from a single Whole Foods location in Princeton, New Jersy, and a basket of products that were chosen arbitrarily. Still, the results show the market's initial reaction to Amazon's announcement to cut prices at Whole Foods may have been a little overblown, Grom suggests.
"We will continue to monitor the situation going forward, but our initial checks suggest that Amazon's bark may be greater than its bite," Grom wrote in the note.
Amazon announced last week that it would start offering lower prices at Whole Foods on "a selection of best-selling grocery staples" starting Monday, and named 15 items that would get discounted. When CNBC visited a Whole Foods store in New York City on Monday, a staff member said more than 300 products were being discounted.
Grom's item list included popular drinks like Vitamin Water and La Croix sparkling water, as well as an assortment of dairy and grocery products.
Given Amazon said the price cuts would be rolled out to more products going forward, it's probably too fast to jump to conclusions at this point. But Grom pointed out Amazon is taking a page out of Wal-Mart's old playbook, "announcing a plethora of price actions that on the surface look deep, but in reality only reveal modest reductions," he wrote in the note.