Caleb was from the tribe of Judah (Numbers 13:6). His father was not a Kenizzite according to the people mentioned in Genesis 15:19, rather Kenaz was simply the name of his father (Joshua 15:17). Caleb himself would also have a descendant named Kenaz (1 Chronicles 4:15).
6 Then the people of Judah came to Joshua at Gilgal. And Caleb the son of Jephunneh the Kenizzite said to him, “You know what the LORD said to Moses the man of God in Kadesh-barnea concerning you and me.