Where does Jewish tradition record that? I’d love to check it out. The only thing “Jewish” that I know of which mentions it, and I could be woefully ignorant of other sources, is 2 Maccabees, which says that Jeremiah hid it in a cave under the “mountain where Moses went up.”
http://www.ou.org/torah/tt/5765/bamidbar65/mikdash.htm
...Biblical commentator David Kimchi (the Radak) quoting a non-extant Midrash writes on II Divrei HaYamim 35:3, “Our rabbis of blessed memory said, ‘that (Josiah, the last righteous King of Judah) gave instructions to hide the ark so it would not be revealed (and desecrated) at the time of the (approaching) exile… At the time when Solomon built the First Temple, he (understood through the Holy Spirit that one day) it was going to be destroyed and therefore he constructed a place to hide the ark in winding, hidden tunnels deep below the surface of the earth. And the stone upon which the ark rested covered the opening of that tunnel. Josiah hid the ark there as it is said, “And he said to the Leviyim that taught all Israel… ‘Put the Holy Ark in the House that Solomon King of Israel did build…’” In Bayit Sheini, both the Aron and King Solomon’s fabulous K’ruvim were missing; Kodesh HaKodashim was completely empty...