The World No 36 said in a statement that he is still to recover fully from the two-month-old injury.
The 29-year-old has been a regular at the event and is one of the tournament’s favourites.
Tipsarevic had earlier confirmed his presence at the $450,000 tournament to be held here from December 30 to January 5.
Speaking about his withdrawal, Tipsarevic said: “I have had a difficult three months after injuring my heel. I felt I would recover well in time for the Chennai Open but regret to say that I will not be able to take part in the tournament.
I apologise to fans who have always supported me and waited to watch me play during matches there. Chennai was always my favourite tournament to start the new season.”