It is the latest in a string of espionage cases and comes as ties are increasingly frosty between Taipei and Beijing.
China still sees the island as part of its territory to be brought back into its fold even though Taiwan has been self-governing since the two sides split after a civil war in 1949.
Relations have worsened since Beijing-sceptic President Tsai Ing-wen came to power last May.
The Taipei District Prosecutors Office says it is investigating whether he has violated the National Security Act.
"He may have engaged in recruiting a spy circle, in attempt to obtain classified information," Chang Chieh-chin, a spokesman for the district prosecutor, told AFP.
Chang declined to reveal more details as the probe is ongoing.
Zhou, who is around 30 years old, had attempted to recruit a young official from Taiwan's Ministry of Foreign Affairs, reports say.
"Mainland students should abide by the law while in Taiwan with study as the purpose," it said in a statement, adding that its policy for accepting students from China would not change.
"The government continues to promote mainland students coming to Taiwan and hopes that both sides can cherish and safeguard the results of years of exchanges," the council said.
The case comes a day after the island's National Security Bureau director-general Peng Sheng-chu told lawmakers Chinese espionage is "more serious than before".
The Investigation Bureau is working on a draft bill aimed at preventing security breaches, but it has drawn controversy over the power it may give to counterintelligence agents.
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