Costco shares fell 7 percent Friday on the news.
And now one trading day after Goldman Sachs downgraded Costco, another bank is following suit.
Deutsche Bank on Monday lowered its rating for Costco to hold from buy, saying the competitive advantage from its food business is at risk due to Amazon.
"The Whole Foods Market acquisition represents a game changer with Costco's competitive moat in grocery under greater threat while its digital platform lags peers, putting membership renewal at risk for decline," analyst Paul Trussell wrote in a note to clients Monday. "The pipeline of positive catalysts has played out and the competitive backdrop is intensifying with Amazon & Wal-Mart accelerating in-store and online efforts and innovation."
The analyst reduced his price target for the company to $172 from $187, representing just 3 percent upside from the Friday's close. Shares were down almost 2 percent to $163.88 during early trading Monday.
After the downgrade, seven analysts recommend buying Costco shares and now five have a hold rating. No analysts have a sell rating.
Costco shares enjoyed the support of Wall Street as its stock climbed more than 80 percent the last five years, much more than most other retail stocks. The low-price warehouse club bred loyalty that trumped the online competition facing the industry. Now, analysts believe that may not be enough as this new threat emerges.
Trussell noted that many of the positive catalysts for Costco are now in the past, including the profitability gain from switching to Citibank's Visa credit card, the announcement of its special dividend and its quarterly dividend increase to 50 cents from 45 cents.
On the flip side, not everyone on Wall Street is jumping ship. Cowen reiterated its outperform rating and $190 price target for the retailer on Monday, saying Costco will survive Amazon's onslaught.
"Our take is that simple competitive advantages form a defensive moat, for now, vs. AMZN Prime's unstoppable rise," Cowen analyst Oliver Chen wrote in the report. "We believe COST's vertical integration capabilities, low price leadership given a fixed low merchandise margin model, & gas and organic food penetration are factors which will drive continued consistency in the generation of positive physical store traffic."
Costco did not immediately respond to a request for comment for this story.
— CNBC's Michael Bloom contributed to this story.