Batsman Steve Smith will now join the squad in Sri Lanka as cover, while Travis Head is set to captain the side at Colombo's R Premadasa Stadium.
Marsh sustained a direct blow to the groin during training earlier this week and is experiencing pain and discomfort which is restricting his movement, the board added.
"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," CA said in a statement.