The accident in New South Wales on 26 December had already killed her parents, sister and the other driver.
The actress, 29, played Hope Morrison in the soap.
Her life support was switched off last week and she died on Wednesday morning local time, said St George Hospital in Sydney.
“The family has asked for privacy during this very difficult time,” it said in a statement.
Jessica’s parents Lars, 69, and Vivian, 60, were killed instantly in the crash and her sister Annabelle, 21, died in hospital three days later.
Australian police are still investigating the crash, which also killed 50-year-old Craig Whitall, who was driving the other car.
At the time of the crash, authorities said they were examining whether Mr Whitall’s car had been on the wrong side of the road.
Last week, hundreds of people attended a funeral service for Lars, Vivian and Annabelle Falkholt in Sydney.
Vivian Falkholt’s brother Paul Ponticello spoke at the funeral, saying he had thought he and his sister “would grow old together”