Vitug's book deals with allegations of corruption against judges of the country's Supreme Court.
The International Federation of Journalists has urged the Philippines government to investigate the death threats.
Vitug reportedly received a message in her mobile phone that read as: "Your kind is the reason why journalists are being killed. Ampatuan had valid reason to kill those journalists. I wish you were one of them." Governor Ampatuan is associated with a massacre of 32 journalists in 2009.
Vitug also faces a defamation suit filed by Justice Presbitero Velasco for an article she wrote about him last year.