In buying the e-commerce company last year, Wal-Mart has hoped to beef up its online ordering offerings, bringing in Jet's co-founder and CEO Marc Lore, who now leads all of Wal-Mart's e-commerce operations.
Jet wasn't immediately available to comment.
"What's fresher than fresh?" Story wrote in release announcing the partnership with Jet. "Having healthy produce dropped at your door — and you don't even have to be home to receive it. This is the magic of Jet.com."
Jet will sell select grocery items at the New York Story location for six weeks. There also will be a number of in-store events with chef Mario Batali and makeup guru Bobbi Brown, among others.
Shechtman, a former brand consultant for Kraft and TOMS shoes, founded Story in 2011. The 2,000-square-foot "start-up store" in Manhattan features a rotating line-up of merchandise, which changes every four to eight weeks, the company says.
Jet's physical debut comes at a time when e-commerce giant Amazon has been investing more in its AmazonFresh business, and testing brick-and-mortar locations to expand its reach.
One store concept, called AmazonFresh Pickup, is a drive-in-type grocery store for Prime members that lets users shop online, reserve a time to pick up the groceries and have them loaded into their car at the store. Amazon also plans to boost the number of physical book stories it operates, and is testing a smart convenience store, Amazon Go, near its Seattle headquarters.
Meanwhile, Wal-Mart has been rapidly expanding its own online grocery business and concentrating on the so-called click-and-collect model, which allows consumers to pick up their orders at stores.
Last year, Wal-Mart announced a partnership with Uber and Lyft to delivery groceries to customers' homes.
While e-commerce is the fastest growing portion of the food retail business, few shoppers buy their groceries online. Wells Fargo Zachary Fadem estimates that just 1 to 2 percent of total grocery spending occurs online.
Since Lore's arrival at Wal-Mart, the big-box retailer has been beefing up its digital operations, recently adding to its portfolio women's clothing retailer Modcloth, for $150 million, and outdoor recreational retailer Moosejaw, for $50 million.
—CNBC's Jeff Daniels contributed to this report.