The children are two 3-year-old girls and a one-year-old boy, all of whom travelled frequently between Taiwan and China with their parents. The mother of one of the children was also diagnosed with kidney stones. The link between Chinese melamine-tainted baby formula and the disease has yet to be confirmed by lab tests, however.
Four children have died and thousands have been affected by melamine-tainted dairy products in China since early September.
Taiwan banned import and sales of Chinese dairy products on September 18. The ban was later extended to Chinese-produced Nestle products.
Taiwanese Health Minister Lin Fang-yue resigned on Thursday over a mishandled recall of melamine-tainted products.
So far, over 20 countries have either banned or restricted imports of Chinese dairy products, including Australia, New Zealand, Indonesia, and Japan.