The man, a college student identified only his surname Yen, was arrested during a raid by police in New Taipei City, police said.
Last month 21-year-old Cheng Chieh attacked passengers on a subway train killing four and wounding two dozen others in a terrifying rampage that shocked a country otherwise proud of its low violent crime levels.
Yen began a Facebook group titled "Cheng Chieh fans group" on May 21, just hours after the deadly attack.
The page was pulled down after web users alerted Facebook to its content but Yen put a further two pages up on the social networking site.
"The suspect has admitted to his wrong-doing and told us that he regrets what he has done," Chiu Chen-ti, an officer from a Taiwanese police unit tasked with computing crimes, told AFP.
Yen allegedly posted statements backing Cheng's killing spree.
"The suspect claimed he did this only for fun, but what he did has fuelled the public's fear over the stabbing spree," officer Chiu said, adding Yen faces up to two years in jail if convicted.
It is not the first time police have arrested people for posting online comments following Cheng's killing spree.
Around 20 people have been questioned for threatening copycat attacks or been detained in "preventive" arrests. All have since been released on bail.
Shortly after his arrest, the lone attacker Cheng "told the police that he had wanted to do a 'big thing' such as this since his childhood," a police officer said.
Authorities have since reinforced police deployment on the busy subway system, which transports around 1.85 million visitors per day.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.