The Russian warships were "detected sailing from south to north in the waters off our eastern coast" as of 11 pm local time (1500 GMT), it said in a statement on Tuesday.
Taiwan's military monitored their movements and "dispatched aircraft, ships and (activated) shore-based missile systems to keep watch", it added.
The ministry did not say how far the warships were from Taiwan's coast.
Self-ruled Taiwan reports a near-daily presence of Chinese vessels near its waters. China claims the island as its territory and has vowed to take it one day, by force if necessary.
The presence of Russian warships is unusual, however.
Russian state news agency Interfax reported on Tuesday that Russia's "detachment of Pacific Fleet warships entered the Philippine Sea after crossing the South China Sea".
The warships were performing tasks as part of a long-range sea crossing, which included "a simulated naval battle to repel a missile attack of a simulated enemy from the sea", Interfax said.
Like the United States -- its top ally -- Taiwan has imposed sanctions on Russia over the invasion of Ukraine, covering exports such as computer technology and machinery products.
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