LEN said in a statement that its disciplinary panel met on Thursday to conduct a hearing with those involved and found that the inscription on the T-shirt "constitutes a clear political action in violation of the LEN Guidelines for Safety and Security at LEN."
Cavic, who was born in Anaheim, California, and lives in Islamorada, Florida, had been due to swim in the 100m freestyle heats on Friday and had the fastest entry time for the 100m butterfly heats on Saturday.
Cavic, 23, was sixth in both the 50m and 100m butterfly at the 2007 World Championships in Melbourne.
The 100m butterfly is an Olympic event but the 50m butterfly is not.