The Australian fast bowler was forced to leave the field following his third over of the day on Saturday and was later diagnosed with a torn stomach muscle.
"I am bitterly disappointed. I've worked really hard on my fitness and have basically gone through the past three seasons unscathed, so to miss this tour now is a major blow," Lee said.
"I pretty much knew from my first ball this morning that something was wrong. There are times when I have stiffness and I can pretty much bowl through it, that's part and parcel of bowling but this certainly felt worse.
"But hopefully we've identified the problem early and it won't turn into a bigger problem."
Lee is the fourth Australian player to pull out of the tour of India, following injured pacemen Glenn McGrath and Jason Gillespie and middle-order batsman Darren Lehmann.
The world champions leave for India on October 22. The triangular one-day tournament, which also includes New Zealand, will be held from October 23 to November 18.
