Witnesses said a hail of bullets from occupation forces on Thursday turned the vehicle into a ball of fire.
Iraqi policeman Fuad al-Hamdani said four civilians were killed in the unprovoked attack.
People have been leaving Falluja following major US airstrikes on the town, 50km west of Baghdad.
No one was able to explain why soldiers fired at the vehicle and the US military said it had yet to receive information on any incident in the area.
Aljazeera's correspondent in Falluja, Abd al-Adhim Muhammad, said 24 Iraqis were wounded during the US bombardment on Wednesday night.
Residents have reported sporadic bombings but said there had been no resumption so far of the massive artillery barrage and air strikes that shook the city of 300,000 on Wednesday.
None the less, US commanders around Falluja have been appealing for more firepower.
Explosions and fires kept Falluja
illuminated on Wednesday night
The Pentagon, in a reversal of policy favouring lighter units, said it was sending dozens of main battle tanks and other armoured vehicles.
ِAbout two dozen heavy M1A1 Abrams tanks will attempt to end the siege within days.
Appeal for calm
But UN Secretary-General Kofi Annan appealed to US President George Bush to show restraint in Falluja.
"The more the occupation is seen as taking steps that harm the civilians and the population, the greater the ranks of the resistance grows," Annan told a news conference in New York.
Occupation forces have surrounded Falluja since the public killing there of four US security guards.
Hundreds of Iraqis have died in the ensuing attempt to wipe out resistance in the town, with some doctors putting the toll at around 600.