Trade friction is emerging as the latest threat to the U.S. dollar’s position at the heart of the global financial system.

For decades, central banks have held the bulk of their foreign-exchange reserves in the dollar, reflecting the dominant role the U.S. and its currency have played in global trade. As the U.S. pulls back from partnerships while countries like Mexico and Japan strike their own trade deals, the dollar’s dominance could be undermined, investors and analysts said. That dominance has been referred to as an “exorbitant...