BERLIN—Tesla plans to halt production at its only large factory in Europe for two weeks because of a lack of parts, a sign of how the fallout from recent attacks on ships in the Red Sea is starting to ripple through the global economy.

Yemen-based, Iran-backed Houthi fighters have launched successive attacks on commercial ships navigating the crucial trade route in recent months, disrupting flows of goods between Asia and Europe and threatening to widen the conflict in the Middle East.