The UAE's state-owned television showed footage of the two veiled women who appeared to be in good health. A UAE diplomat told the channel they would be handed over to the Red Cross in Iraq.
"There is no Indonesian embassy in Iraq so we received them for humanitarian reasons. We are now coordinating with the Red Cross to hand them over," the diplomat said on Monday.
Aljazeera aired footage from the captors showing the two terrified-looking women, each being handed a copy of the Quran.
The Islamic Army in Iraq said last week they had seized the women among a group of 10 captives, which also included six Iraqis and two Lebanese men.
Cleric refuses exchange
They later offered to release the women if Jakarta freed cleric Abu Bakr Bashir, detained on suspected terror links. But the Indonesian Muslim cleric refused to be freed in exchange for the women and Indonesia also said it would not free him.
It was not clear what fate awaited the remaining eight captives.
The Islamic Army in Iraq is believed to be the same group that has held two French journalists hostage for more than a month.
Scores of foreigners have been seized in Iraq since April, few of whom have been women. Most have been released, but about 30 have been killed.