"Tendulkar has not recovered sufficiently from his groin injury," Indian cricket board secretary Niranjan Shah told reporters here.
Tendulkar, 35, picked the injury during India's first-ever one-day tri-series win in Australia earlier this year and although he played in the first Test against South Africa at home, he opted out of the remaining two matches.
The ace batsman did not play in the first seven matches of an ongoing IPL Twenty20 tournament but featured in as many later on.
Shah said the decision was taken following advice from physiotherapist Nitin Patel.
Tendulkar is the world's top one-day batsman, with 16,361 runs, and holds the world records of 39 Test and 42 one-day centuries.
The tri-series in Bangladesh, with Pakistan as the third team, is slated to be held from June 8-14. The Asia Cup will be hosted by Pakistan from June 24 to July 6.