Other portions of Scripture contain Aramaic. Walvoord notes, “A similar use of Aramaic is found in Ezra 4:8-6:18; 7:12-26; Jer. 10:11; and the two words of the compound name Jegar-Sahadutha in Genesis 31:47.”
This section is in Aramaic because it is directed to the Gentile nations. Aramaic was the lingua franca (“common language”) at the time. Miller writes,
Since Aramaic was the lingua franca of this period, it seems logical that Daniel would have recorded most of his memoirs in that language. In fact, Aramaic probably was the means by which he normally communicated. Official decrees were issued in Aramaic so that people in all parts of the empire could read them, and it is not surprising that chap. 4 was written in this language. Moreover, all the accounts in chaps. 2–6 concern Gentile kings whose activities would have been of interest to a world audience, and so this material was written in a language that non-Jews could understand. Finally, the messages concerning the four Gentile kingdoms of chap. 7 (and chap. 2) involved not only Israel but the whole world and therefore were issued in Aramaic.
Whereas chapters 2-7 deal with the Gentile nations, chapter 8-12 are written in Hebrew, because these deal with Israel’s fate under Gentile rulers.
 Walvoord, John F. Daniel: The Key to Prophetic Revelation. Chicago: Moody, 1971. Languages.
 Miller, Stephen R. Daniel. Vol. 18. Nashville, TN: Broadman, 1994. New American Commentary. See “5. Language.”