Travis Head took over the captaincy duties for the encounter against the Irish with Marsh said have injured his groin in training.
"He (Marsh) is experiencing ongoing pain and discomfort which is restricting his movement," a Cricket Australia statement said.
"Scans have confirmed internal testicular bleeding, and he will require a period of rest and rehabilitation. His return to play will be guided by symptom resolution and medical advice.
"Standby player Steven Smith will travel to Sri Lanka as cover to acclimatise and prepare, should he be required."
Smith last represented Australia in the shortest format in February 2024 but looked was in good form in Big Bash League playing for the Sydney Sixers.
The 36-year-old plundered 299 runs at 59.80 and a strike-rate of 167.97 in six innings in the franchise tournament.
Australia have already lost fast-bowling duo Pat Cummins and Josh Hazlewood ahead of the global tournament due to injuries.
South Africa needed a second Super Over against Afghanistan to emerge victorious in one of the most drama-filled T20 World Cup matches ever played in Ahmedabad on Wednesday.
Pakistan avenged their shock T20 World Cup defeat to the United States from two years ago with a commanding 32-run Group A victory in Colombo on Tuesday, powered by Sahibzada Farhan's half-century and a dominant spin performance.
Sri Lanka have suffered a huge blow after spinner Wanindu Hasaranga was ruled out for the remainder of the T20 World Cup due to a hamstring injury.
Tim Seifert and Finn Allen produced a record-breaking opening stand as New Zealand cruised to a 10-wicket victory over the United Arab Emirates in their T20 World Cup Group D clash in Chennai on Tuesday.
