Falkholt, 27, appeared on TV soap Home and Away in 2016, playing the character of Hope Morrison.
She and her sister Annabelle, 21, were seriously injured in the highway crash near Ulladulla, New South Wales.
Home and Away cast members have been sending support to the actress, who appeared in several films and TV shows.
Jackson Heywood, who plays Brody Morgan, posted a picture on Instagram saying: "Much love darlin. Im with ya."
Olivia Deeble, who plays Hope's relative, Raffy, asked fans to send "all your love and healing" to the family.
A spokesperson for Channel Seven, the Australian broadcaster of the show, said the news was difficult to comprehend and "especially tragic" given the Christmas period.
"Although her time on set was brief, once a part of the Home and Away family, always part of the family. Jessica's outstanding talent and professional attitude left an impression on us all."
Falkholt's character first appeared when Hope and Raffy Morrison arrived in Summer Bay.
Hope briefly worked at the garage, but ran away after stealing money from there and from Salt restaurant.
It emerged that her young sister Raffy - actually her cousin - was a sibling of the Morgans, so Raffy stayed in the Bay with them when Hope was jailed for her crimes.
Falkholt's stint on the long-running series came to an end in November 2016. She stars in the US film Harmony, set for release next year.
Motorists who witnessed the crash helped pull the sisters from the burning wreckage, local media reported. They were airlifted to Sydney hospitals.
Police said the three people who died - the sisters' parents and the 50-year-old driver of the other car - had suffered intense burns.
Assistant Commissioner Michael Corboy called the crash "an absolute tragedy" and pleaded for motorists in the state to drive safely.
He said police were investigating whether the car which hit the Falkholts' vehicle had been on the wrong side of the road.
There have been 22 deaths on New South Wales roads since 15 December.