The sentence was awarded by the Supreme Court in May.
Karnan left the Presidency Correctional Home premises around 11.00 am, his wife Saraswati Karnan said.
His wife and elder son, who reached here last night from Chennai, accompanied him.
Karnan was arrested from Coimbatore in Tamil Nadu on June 20 after he had evaded the police for over a month. The Supreme Court passed the six-month jail sentence on him on May 9.
Karnan is the first sitting high court judge to have been sentenced to jail.