Is there a traditional belief in Christianity or Judaism on the cause of death of Moses?

According to the Biblical record, Moses was alone with God, with no man with him, when he died--as commanded by God.

⁴⁸And the LORD spake unto Moses that selfsame day, saying, ⁴⁹Get thee up into this mountain Abarim, unto mount Nebo, which is in the land of Moab, that is over against Jericho; and behold the land of Canaan, which I give unto the children of Israel for a possession: ⁵⁰And die in the mount whither thou goest up, and be gathered unto thy people; as Aaron thy brother died in mount Hor, and was gathered unto his people: ⁵¹Because ye trespassed against me among the children of Israel at the waters of Meribah-Kadesh, in the wilderness of Zin; because ye sanctified me not in the midst of the children of Israel. ⁵²Yet thou shalt see the land before thee; but thou shalt not go thither unto the land which I give the children of Israel. (Deuteronomy 32:48-52, KJV)

After being commanded to go to die, the record states the following:

¹And Moses went up from the plains of Moab unto the mountain of Nebo, to the top of Pisgah, that is over against Jericho. And the LORD showed him all the land of Gilead, unto Dan, . . . ⁴And the LORD said unto him, This is the land which I sware unto Abraham, unto Isaac, and unto Jacob, saying, I will give it unto thy seed: I have caused thee to see it with thine eyes, but thou shalt not go over thither. ⁵So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD. ⁶And he buried him in a valley in the land of Moab, over against Bethpeor: but no man knoweth of his sepulchre unto this day. ⁷And Moses was an hundred and twenty years old when he died: his eye was not dim, nor his natural force abated. ⁸And the children of Israel wept for Moses in the plains of Moab thirty days: so the days of weeping and mourning for Moses were ended. ⁹And Joshua the son of Nun was full of the spirit of wisdom; for Moses had laid his hands upon him: and the children of Israel hearkened unto him, and did as the LORD commanded Moses. ¹⁰And there arose not a prophet since in Israel like unto Moses, whom the LORD knew face to face, ¹¹In all the signs and the wonders, which the LORD sent him to do in the land of Egypt to Pharaoh, and to all his servants, and to all his land, ¹²And in all that mighty hand, and in all the great terror which Moses showed in the sight of all Israel. (Deuteronomy 34:1-12, KJV)

Now there are some obvious problems with that final chapter, from a human perspective. Seeing as no one but God is recorded as present with him, no one knows where Moses was buried, and it was God who buried him, we have no human witness of the event. Further, if Moses did write this chapter, how could he have known what would take place after his death? But if Moses was not the writer, how could the writer have known where Moses went and what had become of him? Either way one approaches this, the only possibility for having a reliable source for the information is to have received it from God, who both sees the future and knows all.

In either case, there is no record for the manner of Moses' death beyond that God was with him at that time and it was at God's behest that he had gone there into the secluded mountain to die. And God Himself buried Moses.

In an interesting twist, perhaps after three days in his tomb to symbolize the resurrection of Christ, for whom Moses had been a type, God then sends Michael to raise Moses to life, as recorded in the book of Jude.

Yet Michael the archangel, when contending with the devil he disputed about the body of Moses, durst not bring against him a railing accusation, but said, The Lord rebuke thee. (Jude 1:9, KJV)

Moses is seen in the New Testament as speaking with Jesus on the mount of transfiguration.

And there appeared unto them Elias with Moses: and they were talking with Jesus. (Mark 9:4; cf. Matthew 17:3; Luke 9:30)

So sometime shortly after Moses had died, he was resurrected and taken to Heaven.

Conclusion

Nothing in the record indicates the cause of Moses' death, beyond the fact that God had ordered it, and since no human was there present to witness it there is no possible way of knowing its cause. Any human tradition or belief about it amounts to pure speculation. We simply do not, and cannot, know.