"Behold, I will stir up the Medes against them, which shall not regard silver; and as for gold, they shall not delight in it. Their bows also shall dash the young men to pieces; and they shall have no pity on the fruit of the womb; their eye shall not spare children." (Isaiah 13:17-18)
This verse clarifies the context. Primarily, God is predicting the fall of the Babylonian Empire through the rise of the Persian Empire. Cyrus the great conquered the larger Median Empire, and many of its laws and practices greatly influenced the Persian Empire. Even the first king put in charge over Babylon under King Cyrus was a Median (Daniel 5:31). Perhaps this is why God mentions Babylon's conquerors as being those of Media and not Persia.
In his conquest of the Assyrian Empire, Nabopolassar allied himself with the armies of Media. His son, Nebuchadnezzar, was married to Amytis, the daughter or granddaughter of Cyaxares (the Median king who aided Babylon in the overthrow of Assyria). In light of this reality, God's prediction of Media's victory over Babylon carries with it extra force. Before Babylon had even risen to power and prior to her alliance with Media, the Lord clearly predicted by whom He would accomplish her downfall. The allies upon which Babylon would lean for support would be the very ones to terrorize her in the end.