At the end of their rule, Pandavas decided to retire. It was time for them to bid good bye to civilization. Arjuna died during the final journey of Pandavas and it is mentioned in the Mahaprasthanika Parva.
Arjuna followed his wife, Draupadi, and brothers to the great snow-clad mountains in the Himalayas. Draupadi slipped and fell as they started climbing the Himalayas. Sahadeva fell next and died. Third to fall was Nakula. Arjuna fell next.
Bhima soon realized that Arjuna had fallen and was about die. He asked to Yudhisthira as to why Arjuna had fallen as he had never performed any evil.
Yudhisthira told Bhima that Arjuna had reaped the fruits of his actions. He had thought himself to be the best archer in the world. But he was envious of all other archers in the world. His insecurity was his sin.
The brothers who had decided to give up all ties climbed the mountain leaving Arjuna behind.
Arjuna died soon.