According to the NET translators' notes,
Scholars debate the appropriateness of this verse to this context.
Many see it as a gloss added by a postexilic scribe which was later
incorporated into the text. Both R. E. Clendenen (“Discourse
Strategies in Jeremiah 10, ” JBL 106 : 401-8) and W. L. Holladay
(Jeremiah [Hermeneia], 1:324–25, 334–35) have given detailed arguments
that the passage is not only original but the climax and center of the
contrast between the LORD and idols in vv. 2–16. Holladay shows that
the passage is a very carefully constructed chiasm (see accompanying
study note) which argues that “these” at the end is the subject of the
verb “will disappear” not the attributive adjective modifying heaven.
He also makes a very good case that the verse is poetry and not prose
as it is rendered in the majority of modern English versions.
This passage is carefully structured and placed to contrast the LORD who is living and
eternal (v. 10) and made the heavens and earth (v. 12) with the idols
who did not and will disappear. It also has a very careful concentric
structure in the original text where “the gods” is balanced by
“these,” “heavens” is balance by “from under the heavens,” “the earth”
is balanced by “from the earth,” and “did not make” is balanced and
contrasted in the very center by “will disappear.” The structure is
further reinforced by the sound play/wordplay between “did not make”
(Aram לָא עֲבַדוּ [la’ ’avadu]) and “will disappear” (Aram יֵאבַדוּ
[ye’vadu]). This is the rhetorical climax of Jeremiah’s sarcastic
attack on the folly of idolatry.1
The Faithlife Study Bible commentators point out,
While the switch to Aramaic here is unexpected and unusual, the chiasm
structuring the sentence suggests it may be a popular saying that uses
wordplay that would not have been possible in Hebrew. Aramaic was in
use at the time as an international diplomatic language (see Isa
36:11) and was known by the educated elite of Judah.2
From the various sources cited, it may have been a Aramaism that best made sense in Aramaic, similar to the use of Latin statements (e.g. quid pro quo) in modern English. Then again, it could have been a scribal gloss.
The other possible explanation is that Aramaic was the language of diplomacy and Jeremiah made a statement that the Israelites should say to their Babylonian captors when they ended up in future exile. This doesn't seem likely, however, and has little scholarly support.
1 Biblical Studies Press, The NET Bible First Edition Notes (Biblical Studies Press, 2006), Jer. 10:11.
2 John D. Barry, Michael R. Grigoni, Michael S. Heiser et al., Faithlife Study Bible (Bellingham, WA: Logos Bible Software, 2012), Jer. 10:11.