In a statement, police said they had arrested a "man in his late 20s" on Tuesday "in connection with investigations into offences related to incitement of violence".
The statement did not name the man or give details of the offence, but said that he was released on bail pending further investigation.
Local media identified him as Abdul Malik Ghazali, 27, who posted a series of comments on the social networking site critical of how Singapore is hosting the inaugural Youth Olympic Games (YOG)
The August 14-26 event, held for competitors aged from 14 to 18, has generated limited public interest, with many events blighted by empty seats and the host country's athletes faring badly.
Vivian Balakrishnan, the minister for community development, youth and sports, has come under particular fire from online critics over the games.
Abdul Malik's postings on his own Facebook page and on a separate group account called "I hate the Youth Olympic Games Organising Committee" are also critical of Singapore's ruling People's Action Party (PAP)
Abdul Malik, who works for a company specialising in wood and flooring, said on his Facebook page that he was arrested "due to my involvement in anti-YOG and anti-PAP Facebook pages".
One of his postings highlighted recent floods in Singapore, the escape of detained terror suspect Mas Selamat Kastari, the amount of money spent to host the games and reports of the poor standard of food served for games volunteers.
He said it was time to "burn" the sports minister and the PAP. "Rally together and vote them out!!!" he wrote.
Abdul Malik said in comments published Wednesday by The New Paper that "the comment is a metaphor".
"I did not intend for it to be taken literally. I did not mean for someone to actually burn," he said.