A spokesman for the Polish-led multinational division in Iraq, Lieutenant Colonel Artur Domanski, said on Wednesday engine failure caused the crash about 8km from Karbala.
Domanski confirmed the fatalities, adding that another four soldiers were also injured in the "emergency landing".
The army chief-of-staff Colonel Zdzislaw Gnatowski added that the injured had been hospitalised in Baghdad and Karbala, but could not pin down the precise cause of the accident.
On Tuesday, the Polish Defence Minister Jerzy Szmajdzinski announced that his country planned to cut the size of its force in the US-led coalition in Iraq from 2400 troops to 1700 in mid-February.
The crash comes as Aljazeera obtained a videotape of a group calling itself the 1920 Revolution Brigades – an armed wing of the Iraqi National Islamic Resistance.
A still image from a video tape
showing an attack on a US base
The tape shows two anti-US fighters setting up a Katyusha rocket launcher and the consequent attack on a US forces and Iraqi National Guard camp in al-Miqdadiya – a town north of Baquba.
Raining mortars down on the camp, the video also filmed the US military response to the attack.
In another incident, sources told Aljazeera that three armed fighters belonging to the Base of Jihad in the Land of Two Rivers armed group were killed in clashes with US forces in Al-Maqdadiya, north of Baquba.
Sources said a group leader called Abu Thur was among those killed.