Then the people of Judah came to Joshua at Gilgal. And Caleb the son of Jephunneh the Kenizzite said to him...
Joshua 14:6

Caleb was the son of a Kenizzite. Either Caleb or Jephunneh were first generation Israelites. Caleb's mother was probably a native of Judah, but that didn't make him an Israelite. His faithfulness did.