HONG KONG—Economic woes in Europe and the accompanying decline in the euro are already digging into the profits of Asia's manufacturers. The worry is that the pain will spread more broadly if European demand for Asian exports falters.

Companies based in Asia that sell everything from sweaters to solar panels in Europe are feeling the pinch already. Orders placed last year when the euro was 20% stronger against local currencies are now forcing Asian businesses to take losses or renegotiate prices with European customers.

...