The 18-year-old, who made a big impression during India's 4-3 one-day series defeat by England, suffered the injury during training at the Twenty20 World Cup in South Africa earlier this week.
"He has been advised six weeks' rest," board secretary Niranjan Shah told Reuters.
"We will decide on a replacement in a day or two."
Chawla was named in the 15-man squad along with off-spinners Harbhajan Singh and Ramesh Powar for the first three ODIs in the seven-match series which begins next Saturday.