Suryansh Shedge has been named as his replacement, with Reddy's absence leaving India short of a frontline pace-bowling all-rounder for the series.
Reddy reported discomfort in his left quadriceps following the third one-day international against Afghanistan on Saturday and has been advised to undergo a period of rehabilitation, the BCCI added.
Shedge, 23, comes in as a batting all-rounder and got the call-up after scoring 147 runs in five matches for India A in the recently concluded tri-series in Sri Lanka.
India face Ireland in two T20Is in Belfast on June 26 and June 28 before travelling to England for a five-match series in July.