The U.S. supermarket chain partnered with Silicon Valley startup Nuro for the service. The rollout comes after the companies began extensive testing in August of Nuro's R1, a custom unmanned vehicle, during a pilot program in the area.
The driverless R1 uses public roads and is used only to transport goods.
The service would be available only in Kroger's Scottsdale Fry's Food Stores for now, for a flat fee of $5.95 and no order minimum, according to the company.
The Kroger-Nuro partnership is the latest effort of supermarket chains to snatch a larger share of the U.S. grocery delivery market to tap into record high consumer sentiment.
Walmart Inc. (WMT - Get Report) has been expanding aggressively in the space. The multinational retailer said last month it would partner with Ford Motor Co. (F - Get Report) and delivery service Postmates Inc. to deliver groceries and other products that could one day be powered by autonomous vehicles.
Amazon Inc. (AMZN - Get Report) will soon be using drones to deliver packages in certain national and international locations, according to The Wall Street Journal, and the e-commerce behemoth created a team to focus on driverless vehicle technology. But Amazon doesn't intend to build a fleet of autonomous vehicles for now.