Luke 1:36 says that Mary, the mother of Jesus, was a relative of Elizabeth. And yet how is this possible, if one comes from the tribe of Judah, and the other from Levi? Both genealogies of Jesus (in Matthew 1 and Luke 3) trace him back to Judah, the tribe of David. But John was from a priestly family – he was from Levi. I cannot figure this one out.
In Exodus 6:23 we read that that Aaron, the brother of Moses and a Levite, married Elisheba, daughter of Amminadab, and sister of Nahshon. Nahshon was a prince of the tribe of Judah (Numbers 1:7). Thus we have an example in the Old Testament of intertribal marriage – in this case also between the tribes of Judah and Levi – even though it seems to be discouraged in Numbers 36. This may of course not be the only intertribal connection. At any rate, the tribes were not totally segregated, and it is well possible that Mary and Elizabeth were cousins of some sort.
Adds Joey Harris:
Mary's mother may have been from Levi and married a man from Judah. Numbers 36:6-7 implies that the purpose of the laws forbidding intermarriage between tribes was to prevent loss of inheritance (which was mainly, though not solely, through the paternal lineage). The Levites did not own nor inherit anything because they belonged to the Lord.
Anyway, Jesus' lineage contains a good deal of intermarriage outside Israel. The majority of the genealogies in the Bible are paternal. Indeed, Jesus' genealogy is unusual in that it explicitly mentions so many women (most of those mentioned being foreigners) and, in the Matthean genealogy, that it terminates with "Joseph, the husband of Mary, who begat Jesus." Anyway, it's possible that Mary's mother was of Levitical heritage (thus presenting no problems with inheritance passing from one tribe to another) and related to Elizabeth's family, while Mary's father was from Judah, thus passing on that tribal identification to his daughter.