The man was parked on a street in the capital Pretoria at night when his vehicle was set alight and he suffered severe burns, Uber Africa said in a statement.
The company said the attackers were unknown, but it pointed to the metre-taxi business that has suffered due to competition from the ride-hailing app.
“We know that these actions do not represent the entire industry, however, this violence and intimidation against those who choose to use technology apps, like Uber, must stop,” Uber said.
Police declined to comment, while an action group of Uber drivers told local news website enca.com that the victim was targeted in a “turf war between Uber and metre-taxi drivers”.
Since arriving in South Africa in 2013, Uber drivers have faced regular violence and intimidation from traditional meter-taxi operators, who accused them of stealing their jobs.
The San Francisco-based firm said it had requested an urgent meeting with the police minister to address safety concerns.
Attacks on Uber drivers have focused on central Pretoria, downtown Johannesburg, the main rail stations and Johannesburg airport.
Uber has hired private security teams to patrol at some locations, and launched an emergency phone line.
At least one other Uber vehicle has been torched in recent weeks.
Earlier this year, metre-taxi drivers blocked the highway to the airport to protest against Uber.
Several cases of violence against drivers have also been reported in other South African cities.
Uber has expanded rapidly but often faced regulatory hurdles and protests in countries including Germany, Spain and Hungary.
Critics and competitors say it dodges taxi regulations.