BERLIN— Deutsche Post DPW.XE +0.39% DHL AG said it would use a drone to deliver medication to a German island in the North Sea, marking the first routine drone delivery to customers and another step in the rapid advancement of the technology.

DHL said Wednesday that as part of a month-long feasibility project, it will start using unmanned aircraft this week to carry medicine from the harbor town of Norddeich, Germany, to the small island of Juist. Each day—depending on weather—the drone will fly autonomously on a preprogrammed seven-and-a-half-mile route, the first routine missions in Europe in which a drone will operate beyond the pilot’s eyesight, DHL said.

DHL’s plans follow those of Amazon.com Inc. AMZN +0.12% and Google Inc.,GOOGL +1.34% which have each tested their own delivery drones. Those U.S. Internet companies have said the routine deployment of the devices is years away—in part because of regulatory challenges—but DHL is hoping to demonstrate that the technology is ready for some real-world applications.

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