Strathclyde Police detained Bird as part of their Operation Rubicon inquiry into claims that witnesses lied under oath during the perjury trial of Sheridan in 2010.
The Crown Office said that Bird was arrested on suspicion of attempting to pervert the course of justice, as well as breaches of the data protection acts.
Andy Coulson, Bird's former boss, was arrested earlier in the year on suspicion of lying in court during Sheridan's trial. He was charged with perjury in May, but vigorously denies any wrongdoing.
Bird's former news editor on the Scottish News of the World, Doug Wright, was also arrested under Operation Rubicon two weeks ago.
Wright has been charged with perjury, conspiracy to intercept voicemail messages and other breaches of the data protection acts.
Bird is still being questioned by police and has not been charged with any offence as yet.
In December 2010, Sheridan was convicted of committing perjury when he won a £200,000 defamation action against the News of the World in 2006, after the paper published allegations about his sex life. He was released in January 2012, a year into his sentence.