Fire crews were forced to use special breathing kit while tackling the blaze, due to the toxic gases released by the burning lithium-ion battery.
To stop the fire, the firefighters had to cool the battery, before cutting through the power supply with a circular saw.
But this released huge clouds of smoke into the air, and meant the $120,000 car was completely written off.
A statement from the Landeck fire service, who dealt with the blaze, said: 'The fire fighting - which could only be carried out under severe respiratory protection - was difficult because the vehicle was repeatedly on fire.
"It was only after cutting the power supply from the high-performance batteries that it was possible to finally fight the fire.
"Since lithium batteries are used, the manufacturer recommends that the vehicle be parked under 'quarantine' for 48 hours, so that no new fire can break out."
Electric car fires are difficult to extinguish, and Tesla admits that they can take up to 24 hours to fully put out.
Unlike petrol and diesel car fires, which once extinguished are out, lithium-ion batteries can easily reignite once alight.
Huge amounts of water are needed to cool the battery, then the power cables must be cut - which puts firefighters at risk of electrocution.
The toxic gases released from the battery add an extra layer of risk.
In its safety manual, Tesla writes: "A burning or heating battery releases toxic vapours.
"These vapours include sulphuric acid, oxides of carbon, nickel, aluminum, lithium, copper, and cobalt.
"Responders should wear full personal protective equipment (PPE), including self-contained breathing apparatus (SCBA), and take appropriate measures to protect civilians downwind from the incident."