The crash occurred around 1am when a German-made car veered into the oncoming lane and slammed head-on into the truck in the southern part of the 16.4-kilometre tunnel, Uri cantonal police said.
The car immediately caught fire and the driver, who died at the scene, was severely burned, police said.
The driver of the truck, which was not carrying a load, was taken by ambulance to a hospital in Faido in the canton of Ticino.
Police said the fire burned the car and its driver so severely that investigators have been unable to determine the identity of the victim.
The licence plates were also destroyed in the blaze, police said.
The Gotthard damage protection service was able to quickly put out the fire, however, the tunnel was closed to traffic until around 8am.
A little more than 11 years ago 11 people lost their lives after a fire in the Gotthard tunnel caused by the collision of two trucks.
A further 128 people were injured in the incident which forced authorities to rethink safety measures for the tunnel, the third longest of its kind in the world.
Meanwhile, another person died when a car caught fire after flipping upside down in Birmenstorf, in the canton of Aargau early on Thursday.
The car had failed to negotiate a roundabout, cantonal police said.
A 19-year-old Swiss man was able to escape the car, which then caught fire, but another man was caught inside, police said.
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Fire fighters tried to rescue the unidentified man, police said, but he died at the scene.