The Ark was not listed in the spoils of war that the Bablyonians carried away from Jerusalem.
What happened to it?
It was the central item in the Temple and could hardly have been overlooked.
Well, tradition has it that Jeremiah hid the Ark:
"It was also in the writing that the prophet,
having received an oracle,
ordered that the tent and the ark should follow with him,
and that he went out to the mountain where Moses had gone up and had seen the inheritance of God.
And Jeremiah came and found a cave,
and he brought there the tent and the ark and the altar of incense,
and he sealed up the entrance."
2 Maccabees 2:4-5.