The 75-year-old Shadrake was arrested at a hotel on Sunday, a day after his publisher and the Singapore Anti-Death Penalty Campaign held a private launch for his book. He had been due to leave on Monday for the Malaysian state of Penang, where he is based.
After the book's Singapore launch on Saturday, Shadrake told the AFP news agency that he expected trouble but felt the authorities were not going to take action.
"If they do anything, it'll just draw more attention to it all, and they have no defence," he said.
Book 'not banned'
|Singaporean authorities said the book had not been banned in the country [EPA]
Police said he remained in police custody on Monday.
The alleged offences are believed to be linked to the book, Once A Jolly Hangman: Singapore Justice In The Dock, which was released for sale in the country late last month but was taken off shelves less than two weeks later after the MDA contacted the store.
An MDA spokesperson said the book had not been banned but added that the authority would "where necessary, advise book importers and retailers to seek legal advice to ensure that the books they sell do not contravene Singapore laws", local broadcaster MediaCorp said.
The book features interviews with local human rights activists, lawyers and former police officers on various cases involving capital punishment in the city-state, which carries out the death penalty by hanging.
It also contains an interview with Darshan Singh, the long-time chief executioner at Singapore's Changi prison, who has since retired.
In 2005, Shadrake wrote an article based on an interview with Singh that caused an outcry among Australians who were campaigning at the time for convicted Australian drug offender Nguyen Van Tuong to be spared the gallows. Nguyen was hanged in December that year.
Singh subsequently told local paper The New Paper that he had been "tricked" into giving that interview.
The crime rate on the island nation of five million people, which imposes the death penalty for crimes such as murder and a mandatory death sentence for drug trafficking, is among the lowest in the world, and Singapore officials say the death penalty is a key factor in maintaining that.