Lieutenant Ali al-Shammari said the bombs exploded within a few minutes of each other in the vicinity of a car market in Jbeila, near the city of Hilla.
The second blast came as rescue workers were arriving at the scene. Thirteen of the wounded were in serious condition, a hospital source said.
In other incidents of fighting across Iraq, at least four Iraqi policemen and one US soldier was killed.
Aljazeera reported that an American soldier was killed and two others wounded in an explosion in Diyali.
In western and southern Baghdad, four Iraqi policemen, among them an officer, were killed, and 10 others were wounded in two attacks by gunmen.
In the north of Baghdad, police carried out a raid and arrested 36 people, a source in the Iraqi Interior Ministry said. The raid was carried out in the al-Hussainia district.
Two prominent figures have also died in the day's violence. In Baghdad, a source in the Defence Ministry said armed men had assassinated Lieutenant-Colonel Rahim Amin al-Hilfi, an officer of the Badr Brigades.
And unidentified gunmen in Tal Afar killed local municipal council member Abd al Karim Sulaiman al-Ahmad.
Elsewhere Iraqis have gone to the streets to demonstrate. In Riyadh, near Kirkuk, hundreds of Arab residents rallied in protest against the detention of former Iraqi army officer Major-General Nayef al-Obaidi.
US military vehicles have also come under attack during the day. South of Kabala a US vehicle was damaged by an explosive device, and a truck near al-Khalis was set ablaze by a second explosive device.