The girl's parents and brother were taken to hospital and their injuries were not thought to be serious.
The male driver of the Peugeot was arrested and taken into custody. A female passenger was taken to hospital suffering from minor injuries.
The incident happened just before 6.30pm and police, ambulance and fire crews attended.
The Metropolitan Police said the pursuing police car had its blue lights and sirens on when the collision happened.
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The cyclist said the victory was as sweet as his first win as he became the first Briton to win the race three times.
Local police confirmed the explosion, which occurred near Nuremberg.
Temperatures slide a couple of degrees