"Costco has had a great multiyear run and we missed it," he wrote in a report.
"The temptation is to just catch up with consensus and call it a learning opportunity. Our problem is we have not learned anything new about the Costco story to justify an ever greater multiple."
The analyst raised his target price on the Issaquah, Wash., retailer to $230 from $220. The new target indicates a decline of 21% from the Wednesday closing price of $292.43. The stock is trading Thursday off 1.9% at $286.90.
Costco is trading at nearly 35 times estimated fiscal 2020 earnings, the analyst said in the report.
"We look at valuation through several lenses: paying for earnings, ... paying for dividends, for free cash flow and for defensiveness," Fletcher wrote. "In all cases ... Costco is currently overvalued."
Bernstein sees risks to the pace of Costco's growth, in the U.S. and overseas.
These include competition from rivals for members; an economic downturn "big enough to cause members to reevaluate spending and membership fees" and, on the international front, Costco's growth in China "will go more slowly than most investors might expect."