"England captain Eoin Morgan has sustained a small flake fracture to his left index finger," ECB said in a statement.
"Morgan picked up the injury during catching practice... he will not take part in the match (against Australia)... but is expected to make a full recovery and be available for England's opening World Cup match against South Africa."
The ECB did not say if Morgan would play in another warm-up clash against Afghanistan on Monday.
Favourites England begin their World Cup campaign against South Africa on the opening day of the tournament.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)