His Revolution Growth fund will invest $22 million in the company, which three graduates of Georgetown University founded in 2007. With 22 locations in D.C., Maryland, Virginia, Boston and New York, Sweetgreen partners with local suppliers to bring customers fresh, organic produce. The menus reflect the seasons.
(Read more: Kale Caesar! Salads top the menu for workday lunches)
Case says the food industry is "ripe" for change and he could see Sweetgreen being a global brand, much like Starbucks.
"Our belief is bolstered by the success of other innovators that have fundamentally transformed food in America. From Starbucks—a niche Seattle coffee shop that is now worth over $60 billion—to Chipotle, a Denver-based burrito shop committed to high-quality ingredients and a market cap now exceeding $16 billion, the evidence strongly suggests a shift in America's taste for fast-casual dining," Case wrote on the fund's website.
Jonathan Neman told CNBC how he and his two other co-founders hope to expand the business and how they got the attention of and investment from Case and Revolution.
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—By CNBC's Gloria McDonough-Taub