The arrest comes after authorities stepped up censorship and detained dozens of people ahead of last week's 25th anniversary of the crackdown, in which soldiers killed hundreds, by some estimates more than 1,000, protesters.
Authorities in Beijing arrested a 22-year-old surnamed Zhao for using Twitter to "spread news of law-breaking methods", the China News Service said on Monday.
The details given in the report appeared to match the Twitter account of Zhao Huaxu, a student in Beijing, who had posted a plan to use a transmitting station to broadcast information about the Tiananmen crackdown via SMS.
Twitter is blocked in China by a system dubbed the "Great Firewall of China", although some users circumvent controls to use the service. Arrests for comments made on the US service are rare.
A phone number listed for Zhao was not answered on Tuesday, and Beijing police were not immediately available for comment.
Authorities launched a campaign against online "rumours" relayed on domestic social media sites last year which saw hundreds of people, including several prominent government critics, detained.
Separately, police on Monday denied bail to Pu Zhiqiang, a celebrated human rights lawyer detained in May for attending a private seminar about the 1989 crackdown, friends said.
More than 40 journalists, lawyers, scholars and activists were held under various forms of detention ahead of the June 4 anniversary, Amnesty International said, in a larger clampdown than in previous years.