It happened just after 1:30 a.m.
Debra Williams, a spokesperson for Jazz Aviation says three of the crew members and two passengers were taken to hospital, four have since been released.
She said the person who remains in hospital was a passenger on the flight.
Peel paramedics originally said the four crew members suffered minor injuries and were taken to hospital for treatment and clarified that only three crew members were taken to hospital as a precaution.
About 50 other people on the plane were assessed at the scene. The Greater Toronto Airports Authority said passengers were allowed to leave the airport.
Police say the driver has been charged with dangerous driving under the Aviation Safety Act.
The aircraft and the fuel truck were removed from the scene.
Officials said the incident did not impact operations at the airport.
With files from The Canadian Press