"One of the bombs became stuck because of a technical problem, and during its (the aircraft's) return to base it fell on three houses in Baghdad Jadida," security spokesman Brigadier General Saad Maan said in a statement.
The jet was coming back from a bombing run when the accident occurred, Maan said.
Officials said that the blast, which occurred near the Rasheed air base, also wounded at least 11 people.
The Su-25s are robust aircraft designed for ground attack missions, but Iraq's Sukhoi fleet is made up of ageing planes.
The US agreed to sell Iraq 36 F-16 warplanes, but none have been delivered so far.
The first batch of the jets has instead been sent to Arizona, where Iraqi F-16 pilots are training.
One of the pilots, Brigadier Rasid Mohammed Sadiq, was killed in a crash during an aerial refuelling exercise at the end of June.