Brunt was unable to join the rest of the squad, who flew out on Tuesday.
And on Friday, it was confirmed Lynsey Askew had been summoned as cover to support the other bowlers.
"It's disappointing news for us because Katherine is a key player for England. However, we do have quality cover in Lynsey," said coach Richard Bates.
Brunt was a key member of the England side which won the Women's Ashes series against Australia in 2005 but had to return home early from a tour to India that winter after fracturing a bone in her left hand.
She returned to action against India last summer but only played the first Test and two of the five one-dayers because of her back problem.
DD Sports to telecast quadra series: New Delhi: Public broadcaster Doordarshan will telecast live all matches of the second Quadrangular Women's cricket tournament to be played at Chennai on its DD Sports channel.
The Quadrangular series will feature India, Australia, England and New Zealand.
Schedule: Feb 21: 0930-1700 hrs (Live); Feb 24: 0930-1700 hrs (Recording); Feb 26: 0930-1700 hrs (Recording); Feb 28: 0930-1700 hrs (Live); Mar 01: 0930-1700 hrs (Live); Mar 03: 0930-1700 hrs (Live); Mar 05: 0930-1700 hrs (Live).