The police had opened fire to stop the van after a highway chase between Namur and Maisieres, a suburb of the city of Mons.
The child, who was on board the van with her parents, died in the ambulance on her way to hospital.
"The autopsy determined that the cause of death was a bullet that entered the cheek," prosecutor Frederic Bariseau told reporters in Tournai near the French border.
Police have opened an internal investigation to determine the circumstances of the girl's death, Bariseau said.
"We cannot exclude that this bullet came from a police officer's gun," he said.
"The investigation will have to determine whether there were other shots, and from which police officer if it was a police officer, or someone in the van who could have been armed," he said.
Rules of engagement "are strict. Police are free (to open fire) if they deem themselves in danger," he said.
The prosecutor's office initially said on Thursday that the girl had "not died as a result of the police shooting".
In the van intercepted by the police were 30 people including 26 adults, all of Kurdish origin, who are now in custody.
Authorities initially evoked a number of possible causes of death, including illness or reckless driving during the chase.
The prosecutor said the incident began with a routine patrol by police at a parking lot in Namur, the capital of the Belgian region Wallonia.
Police determined that the plates on the van were fake and approached the vehicle, which drove away.
"A first arrest attempt was made in Sambreville when the vehicle pretended to stop and then accelerated," the prosecutor said.
"That's when the police called for reinforcements and why we found ourselves with a fairly large number of police officers," he said.
The shots were fired by police at the end of the chase near Mons, he added.
The death caused a stir on Thursday in the migrant community of Grande-Synthe, near Dunkirk in France, as the girl was a member of a family currently housed there, French authorities said.
The Belgium border region near France has become a magnet for migrants, with many heading towards Grande Synthe or Calais to try to board lorries and reach Britain.
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