The pharmacy market is one of the biggest potential new targets for Amazon.com Inc.

In June, the online retail giant moved into the roughly $800 billion U.S. grocery space by buying Whole Foods Market Inc. Drugs, a $450 billion industry in the U.S., are likewise most often sold from brick-and-mortar stores. Shoppers filling prescriptions frequently pick up toiletries, beauty supplies and dish soap—all retail items Amazon already sells. And the distribution chain for drugs has lots of middlemen whose markups Amazon can seek to undercut.

No wonder shares of drugstore chains CVS Health Corp. and Walgreens Boots Alliance Inc. have dropped sharply since analyst speculation about Amazon entering the pharmacy business intensified last month. On Monday, CVS Health said it would begin same-day delivery in several cities in early 2018, an apparent defensive move. Amazon has never commented on its pharmacy ambitions.