The last mention of the Ark in the Old Testament would be Jeremiah 3:16-18. Here is a note on this passage from the "Believer's Bible Commentary":
3:15-18 These verses anticipate the Millennium. God will give them shepherds according to His heart, who will feed them with knowledge and understanding. There will then be no need for the ark of the covenant because the Messiah Himself will be there. Jerusalem will be the world capital and called The Throne of the LORD. Israel and Judah will be restored from worldwide dispersion and reunited.