Germany is tightening rules to make it harder for non-European companies to buy stakes in German firms without its approval, signaling growing concern in Berlin about China’s push to acquire key technology and know-how.

China’s aggressive plans to purchase assets around the world has forced a series of countries to take steps to screen the investments, many times blocking them. The European Union has recently agreed to establish a common framework to tackle the issue. In the U.S., Congress has moved to strengthen the vetting...