A roadside bomb exploded in the Baghdad Jadida area and a suicide bomber then detonated an explosive vest, the officials said.
There was no immediate claim of responsibility for the bombings, but the Islamic State group carries out frequent suicide bombings targeting members of the country's Shiite majority, whom it considers heretics.
The blasts came two days after another suicide bombing claimed by IS killed six people in western Baghdad.
Iraqi forces are preparing for a push on Mosul, the last IS-held city in the country, after regaining much of the Iraqi territory the jihadist group seized in June 2014.
But IS has maintained the ability to carry out attacks in government-controlled areas even as the jihadist group lost ground, and it is likely to increasingly turn to such insurgent tactics if it loses Mosul.