Stirling suffered the injury when he hit the turf while completing a catch to dismiss Josh Inglis. He later walked out to open for Ireland in the 183-run chase but limped off after facing just one ball.
Uncapped 20-year-old left-handed batter Sam Topping has been named as Stirling's replacement in the squad.
Ireland have lost both their games so far in the tournament and will play Oman on Saturday in Colombo.