Was Moses from the tribe of Dan?

No, Moses was from the Tribe of Levi (Exodus ch.6).

More information:

Moses was a great grandson of Levi. He was born 245 years after the death of Abraham. The time when Moses was born was when the Pharaoh had ordered his people to kill all Israelite male infants because he (Pharaoh) was afraid that the Israelites would become too strong for him (Exodus ch.1-2).

Moses' mother didn't want him to die. So she made a basket for him and put him in it to float in the Nile reeds. He was found by Pharaoh's daughter, who took pity on him (Exodus ch.2) and raised him as her own son. (See: How did Moses know he was an Israelite?)

Moses was forced to flee after killing a cruel Egyptian taskmaster, and went to Midian, where he wedded the daughter of Jethro.

He eventually achieved the highest level of prophecy (Deuteronomy ch.34) and was called upon by God (Exodus ch.3). He brought the Israelites out of Egyptian slavery (Exodus ch.12). He received the Torah from God (Exodus 24:12) and later recorded it in writing (Deuteronomy 31:24). He went up on Mount Sinai for 40 days and nights (Deuteronomy ch.9-10) and brought down the Two Stone Tablets with theTen Commandments (Exodus 31:18). He brought the Israelites into the covenant with God (Exodus ch.19 and ch.24), and he oversaw the building of the Tabernacle (Exodus ch.35-40). He was the humblest of men and the greatest of prophets (Numbers ch.12).

See also:

What problems did Moses face and overcome?