The explosions took place near the Iranian, Egyptian and German embassies in centre of the city.
"They were suicide attacks against the Egyptian and Iranian embassies," said Major General Qassim Atta, spokesman for Iraqi security forces in Baghdad.
According to Iraq Interior Ministry, two of the blasts were in the Mansour district of west-central Baghdad, near the German embassy and Egyptian embassies.
The third blast occurred near the Iranian embassy not far from the Green Zone, which houses many Iraqi government offices and the US embassy.
Many of the dead were said to be employees at a nearby state-run bank. The injured have been rushed to the near-by hospital.