Yes, they're related in a well-established family. [0] gives a good view of the family tree.
And the reason they're so far apart is that they must have migrated there from the north. From Wikipedia [1]:
> The Apachean languages, of which Navajo is one, are thought to have arrived in the American Southwest from the north by 1500 CE, probably passing through Alberta and Wyoming.[14][15] Archeological finds considered to be proto-Navaho have been located in the far northern New Mexico around the La Plata, Animas and Pine rivers, dating to around 1500. In 1936 linguist Edward Sapir showed how the arrival of the Navajo people in the new arid climate among the corn agriculturalists of the Pueblo area was reflected in their language by tracing the changing meanings of words from proto-Athabaskan to Navaho. For example the word dè: which in proto-Athabaskan meant "horn" and "dipper made from animal horn" in Navaho came to mean "gourd" or "dipper made from gourd". Likewise the proto-Athabaskan word ɫ-yáxs "snow lies on the ground" in Navaho became sàs "corn lies on the ground". Similarly, the Navaho word for "corn" is nà:-dą: derived from two proto-Athabascan roots meaning "enemy" and "food", suggesting that the Navaho originally considered corn to be "food of the enemy" when they first arrived among the pueblo people.
And the reason they're so far apart is that they must have migrated there from the north. From Wikipedia [1]:
> The Apachean languages, of which Navajo is one, are thought to have arrived in the American Southwest from the north by 1500 CE, probably passing through Alberta and Wyoming.[14][15] Archeological finds considered to be proto-Navaho have been located in the far northern New Mexico around the La Plata, Animas and Pine rivers, dating to around 1500. In 1936 linguist Edward Sapir showed how the arrival of the Navajo people in the new arid climate among the corn agriculturalists of the Pueblo area was reflected in their language by tracing the changing meanings of words from proto-Athabaskan to Navaho. For example the word dè: which in proto-Athabaskan meant "horn" and "dipper made from animal horn" in Navaho came to mean "gourd" or "dipper made from gourd". Likewise the proto-Athabaskan word ɫ-yáxs "snow lies on the ground" in Navaho became sàs "corn lies on the ground". Similarly, the Navaho word for "corn" is nà:-dą: derived from two proto-Athabascan roots meaning "enemy" and "food", suggesting that the Navaho originally considered corn to be "food of the enemy" when they first arrived among the pueblo people.
[0] http://glottolog.org/resource/languoid/id/nava1243 [1] https://en.m.wikipedia.org/wiki/Navajo_language#History