Salma al Shari, also named as Salma al Barakati, told Okaz newspaper that she began driving as soon as the conservative kingdom lifted its ban on women driving last month.
She said she used it to help her elderly parents with lifts and errands.
She added that she had been repeatedly threatened and harassed by young men their village, Samad in Mecca province.
They told her to stop driving because it was “against the will of God”, she said. But when she chose to ignore them, they set her car on fire earlier this week.
In a video posted to Twitter - a social media platform widely used by Saudis - Ms Shari can be heard screaming as the car goes up in a blaze of flames and smoke.
The 31-year-old told local news organisations that her harassers were “barbaric” for their actions.
The car, driving lessons and licence - for which Ms Shari made arrangements as soon as it was announced the ban would be lifted last year - was a significant investment for the sales cashier, who earns 4000 riyals (£800) a month.
She was previously spending half her salary on a driver.
The majority of Saudis have embraced the 24 June lifting of the driving ban as the dawn of a new era of freedom for women in a country where the male guardianship system effectively renders them second class citizens.
Some women, however, have expressed their fear of a backlash from religious conservatives.
Police said in a statement the fire is being treated as arson and they were searching for the suspects.
Unverified reports said that the Mecca vice governor’s office had offered Ms Barakati an alternative car to use while the investigation continues.
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