BERLIN—Germany is looking for new ways to power its economy as the traditional growth engines of manufacturing and exports falter. But the country’s outdated internet is acting as a bottleneck.

The sorry state of the online network has become a national joke and an economic liability. Germany ranks 33rd in the world in average monthly fixed broadband connection speeds, and 47th for mobile, according to Speedtest Global Index. By comparison, the U.S. ranks 7th and 37th, respectively.

The slow speeds are hampering the digitization of swaths of industry and the delivery of products and services to consumers, causing pain for German companies such as media conglomerate Bertelsmann SE, whose portfolio includes online video producer RTL Group, music group BMG and a controlling stake in publisher Penguin Random House.

“Our business is about content and reach, and monetizing the reach,” said Chief Executive Thomas Rabe. “And if the reach is reduced by the lack of technical infrastructure, that is, of course, a problem.”

In Germany, for example, gigabyte connections—which handle more than 1,000 megabits per second—are rare. As a result, streaming ultra-high-definition video can be hit-or-miss outside big cities, with the images sometimes appearing choppy.