The Trump administration signaled that it preferred a weaker U.S. dollar Wednesday, setting off reverberations in markets from New York City to São Paulo to Tokyo.

Past U.S. administrations have typically tiptoed around the subject of a weaker dollar, fearful that explicit views might affect interest rates or scramble cross-border commerce. Treasury Secretary Steven Mnuchin was more overt at the World Economic Forum in Davos, Switzerland, where he stated that a “weaker dollar is good for trade.” Coupled with new tariffs and...