They can likely cut Whole Foods' margins on many items and, through the magic of the warehouse club nature of Prime, offer further discounts to Prime members, incentivizing the choice of Amazon over their competitors. Not all people will we swayed, but some will.
This will shake up the grocery market in many metros, where margins are tight and incumbents are often saddled with tight margins, concerns about real estate, and preexisting debt. Some will spend more to retain customers with extra features like free at-store pickup or cheap delivery, but they won't be able to outmatch Amazon's warchest. The most vulnerable among their competition will fold, allowing customer bases to re-align.