The Diocese said the incident occurred at St. Patrick's Cathedral around 10am on Tuesday, while the church was open for prayer.
"We are saddened to announce the vandalism at St. Patrick Cathedral earlier today," the Texas diocese said in a post.
Pictures show the head of Jesus decapitated on the church altar.
The left hand and arm was also broken off, and lay on the marble ground.
The base of the figure was also disconnected.
Tiny pieces of the statue lay all around the smashed figure.
The diocese said one suspect was detained by police in the incident.
Police are continuing their investigation.
Shock pics show historic Jesus statue decapitated on church altar