"The 'one China' principle remains a political foundation of the US-China relationship. We strongly oppose any official contacts between the United States and Taiwan," ministry spokesman Lu Kang said at a press briefing.
Lee reportedly met with Bolton during his May 13-21 visit to the United States.
Last week, China lodged a representation with the United States about the passing of two US warships through the strategic Taiwan Strait in the South China Sea. Beijing has long opposed the movement of vessels in the Taiwan Strait.
The US, along with many other countries, does not recognise Taiwan as a sovereign nation and officially adheres to the "One China" policy. However, Washington has maintained informal relations with the de facto government of Taiwan despite breaking diplomatic ties with Taipei in 1979.
Beijing considers Taiwan to be part of a united China. Relations between the two sides were cut in 1949 after the remnants of Chiang Kai-shek's forces fled to the island following their defeat on the mainland. Ties were partially restored in the 1980s.