Jordan Neill, already part of the Test squad, will now remain with the team to replace him in the T20Is.
Adair, who hit a 58-ball century against South Africa last year, had shown signs of returning to form with scores of 48, 26 and 33 in T20Is this year.
His recovery timeline means he is expected to return ahead of next year’s T20 World Cup.
Neill, who made his international debut in May before suffering an injury, has been added to provide top-order cover.
National selector Andrew White said losing Adair was “very unfortunate,” but noted the tour will help Ireland test new combinations ahead of the World Cup. He added that left-hander Ben Calitz’s inclusion will offer middle-order variety.
Ireland begin the tour with a Test in Sylhet on November 11, followed by the second Test on November 19 in Mirpur. The three-match T20I series starts on November 27.
