Airport spokeswoman Victoria Lupica says the truck apparently tipped over on a service road near Terminal F around 1 p.m. Tuesday, spilling about 200 gallons of fuel.
Emergency vehicles are on site and cleaning up the spill. Lupica says there are no injuries and no aircraft have been damaged.
The terminal is used by US Airways Express.
US Airways spokesman Morgan Durrant says the spill is affecting flights at 11 of the terminal's 26 gates.
Durrant says some flights are being delayed up to two hours. It's unclear exactly how long the cleanup will take.