Three Americans were among the victims of the blasts at a market and cafe.
The Green Zone, where Iraqi government offices and US forces are based, comes under frequent mortar attack.
But this appears to be the first time militants have managed to carry out suicide bombings in what is supposed to be the safest place in Iraq.
In a statement posted on an Islamic website, the group led by Jordanian militant Abu Musab al-Zarqawi said it was behind the blasts.
The claim could not be independently verified.
