Holcomb landed in Taipei on Sunday "to kick off an economic development trip" in Taiwan and South Korea.
"The Taiwan question has always been the most important and the most sensitive issue at the heart of China-US relations. The Chinese side firmly opposes official US exchanges with the Taiwan region in any form and under any name. We have made serious demarches to the US side on Indiana Governor Holcomb's visit to Taiwan," the ministry said in a statement.
Beijing has called on Washington to "abide by the one-China principle and the three China-US joint communiques, and stop all forms of official interactions with the Taiwan region," it added.
Tensions near Taiwan remain high as China is opposed to any direct foreign official contacts with the island that it considers its sovereign territory. Beijing has repeatedly said that the One China principle is a political foundation of China-US relations and that violations by Washington of its own obligations have been jeopardizing cooperation between the two countries, threatening peace and stability in the Taiwan Strait.