Loren Davis was driving at 100km/h (62mph) on an expressway in Adelaide on Tuesday when she hit the koala as it was crossing the road.
Ms Davis only discovered what had happened to the animal when she reached home and inspected her car.
The koala only had minor abrasions and will be released into the wild soon.
"We're calling him Bear Grylls," said Ms Davis, whose choice of nickname was inspired by the British survival expert and television presenter.
Koalas, which are often mistaken for bears, are in fact marsupials.
Ms Davis told reporters that she had been driving down a dark stretch on the expressway and only saw the koala when her headlights illuminated it.
She said she could not change lanes nor brake because of traffic next to her and behind her, and had "no choice but to hit the koala".
She later pulled to one side to check but could not see the koala anywhere.
Ms Davis drove to her home about 10km away, "feeling upset that I'd killed a koala," she told the Australian Broadcasting Corporation (ABC).
"Once I got home and pulled into the garage I turned on the light to see the damage. I turned around, saw a koala and just screamed."
The koala was still conscious and growled as Ms Davis approached. She and her fiance finally pushed a blanket underneath its dangling arm so that it could push itself up and out of the grill.
Animal rescue volunteers later came by and took the animal for treatment. It is expected to be released soon.
Fauna Rescue co-ordinator Merridy Montarello told The Advertiser newspaper in Adelaide that it was a "very, very lucky koala".
"It's because of the particular size of it [that it survived]... It's just sat itself inside the car."
"Bear Grylls" is not the only koala to have a lucky escape on Australia's roads.
Another koala got stuck head-first in a car grill three weeks ago when it was hit on a road in another part of Adelaide, reported ABC.  In 2011, a koala named Kenny in Queensland also survived under similar circumstances.
In 2014 a koala named Timberwolf survived a 54.5 mile (88km) ride clinging to the bottom of a car, also in Queensland.
However, not all koalas are so lucky - according to some estimates, about 85% of koalas involved in road accidents may die from their injuries.
A koala in Australia has been dubbed "Bear Grylls" after it was hit by a fast-moving car and survived when it got wedged in the car's front grill.