The girl died on the way to hospital, according to the news agency Belga, after the van was stopped by armed police in the western city of Mons.
Officers were reportedly forced to use their weapons when the van tried to run them over, however police were not to blame for the girl's death according to officials.
"It was not police gunfire which caused the death of this girl," Belga quoted Tournai prosecutor Frederic Bariseau, as saying.
The chase began when authorities observed the van being driven in a suspicious manner on a motorway near the city of Namur in the early hours of Thursday morning.
Around 15 police vehicles and 30 officers were involved in the ensuing chase, according to Belga, and 30 people were found in the van, 26 adults and four children.
It said the dead girl and her family were Kurds who had recently been deported from Belgium to Germany and were trying to make their way to Britain via Belgium.