As President Trump uses tariffs as a weapon in his quest to even the score on trade with the world, Asia is emerging as target No. 1. And it’s not just because of China.

Asia is home to seven countries that run the biggest trade surpluses with the United States, Mr. Trump’s go-to yardstick. It has some of the biggest exporters of goods that Mr. Trump promised to tax, like Japanese and South Korean cars, Taiwanese chips and Indian drugs. Many of the region’s countries have become top destinations for Chinese goods and investment, evidence that Mr. Trump cites to accuse China of using a backdoor into the U.S. market.

Mr. Trump’s plan to upend the rules of world trade could hurt Asia because the region relies so much on the global economy. But it will also scramble supply chains and trade flows that are already undergoing change as companies have sought alternatives to China as the source of their goods.

The result could be a domino effect of protectionism, with countries turning inward and raising tariffs in response to American trade barriers, experts said. The upheaval could also generate a new cast of regional alliances and ultimately a reduction in the importance of the United States in trade with Asia.

“There is a risk that the U.S. really overplays its leverage,” said Simon Evenett, a professor at IMD Business School in Switzerland. “The U.S. market is still the biggest in the world but proportionally it is lower than it was 20 years ago.”