TAIPEI—The worst drought in half a century is hitting Taiwan, adding strain to an island that is home to two-thirds of the world semiconductor manufacturing capacity during the worst global chip shortage in recent memory.

The drought’s impact on semiconductor producers, which require voluminous quantities of water to churn out chips, is so far modest as the government creates exceptions for these manufacturers. But companies are starting to make adjustments, and officials have warned that the water shortage could worsen without adequate rainfall.

Taiwan’s semiconductor wafer-fabrication factories, or fabs, account for 65% of global production, according to the research firm TrendForce. Most of that capacity belongs to Taiwan Semiconductor Manufacturing Co. TSM 0.41% , the world’s biggest contract chip maker.