It happened around 11:30 Saturday morning at the Edgemoor Post Office on the 4900 block of Governor Printz Boulevard.
The flames were confined to the truck, but as a precaution the post office was evacuated.
The fire was brought under control within 15 minutes.
No injuries were reported and there was no damage to mail. Several parked cars sustained damage from debris.
A cause for the fire is still under investigation.