The Dow Jones Industrial Average dropped nearly 400 points and U.S. Treasury yields posted their largest daily decline in nearly two years as investors around the globe retreated from risk following signs of political upheaval in Italy.

Six years after the eurozone stepped back from the brink of a breakdown, a violent selloff in Southern European debt bled into broader financial markets, pushing investors toward the safety of the dollar and the Japanese yen, which rallied sharply.

Bank...