The bombs went off almost simultaneously just after noon Monday at a second-hand clothes market in the Bab al-Sharqi area. At least one of the blasts was caused by a car bomb.
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More than 3,000 American troops from the 82nd Airborne Division have arrived in Baghdad in recent days as part of a military buildup to help Iraqi security forces fight sectarian violence.
The U.S. reinforcements are the first to be sent to Baghdad as part of President Bush's controversial new strategy to stabilize the city.
In an interview with the newspaper, "USA Today," Mr. Bush says he will not set a timetable for withdrawing troops from Iraq, because doing so would enable insurgents to adjust their tactics.
Iraq's ambassador to the U.S. Samir Sumaidaie said in a separate interview Sunday that the arrival of more U.S. troops in Iraq will give Baghdad a few more months to reform its security forces.
Sumaidaie warned that a pullout of U.S. troops would create a vacuum that benefits terrorists.
On Sunday, bomb attacks in Baghdad killed at least seven people. Two U.S. Marines also were killed in separate incidents in the western province of Al Anbar.
Some information for this report was provided by AFP, AP and Reuters.