Alan Shadrake, 75, was in Singapore to promote the book and was arrested Sunday, police said in a statement.
He hosted an event Saturday promoting "Once a Jolly Hangman: Singapore Justice in the Dock."
Police said they arrested Shadrake based on a complaint by the government's Media Development Authority and were investigating him for other offenses. They declined to give details.
The attorney-general's office is also seeking contempt of court charges against Shadrake because statements in the book allegedly impugn the impartiality, integrity and independence of the judiciary, a spokeswoman said. She spoke anonymously in line with the attorney-general's office policy.
The contempt of court charges will be heard by a judge at the country's High Court on July 30.
Shadrake's lawyer, M. Ravi, said police have not allowed him to speak to his client yet, and no bail has been set. Shadrake has recently been treated successfully for colon cancer, Ravi said.
Criminal defamation carries a sentence of up to two years in jail, a fine, or both.
A flier promoting the book says it "cuts through the facade of official silence to reveal disturbing truths about Singapore's use of the death penalty," and "reveals the cruelty and imprudence of an entire judicial system."
The media authority said in a statement Monday that it had not banned the sale of the book in Singapore.
Human rights groups including Amnesty International contend Singapore applies defamation laws selectively to silence criticism. The government says restrictions on speech and assembly are necessary to preserve economic prosperity and racial and religious harmony in the multiethnic city-state of 5 million people. It says any statement that damages the reputations of its leaders will hinder their ability to rule effectively.
