Heche suffered "severe anoxic brain injury" and remains in a coma in critical condition due to the incident, which took place last Friday.
The 53-year-old was taken to hospital following the crash in the Mar Vista area of Los Angeles.
It comes shortly after the Los Angeles Police Department confirmed to the PA news agency the incident was being investigated as a felony driving-under-the-influence (DUI) traffic collision.
An LAPD spokesman said preliminary blood tests had revealed the presence of drugs in Heche's system, but added that additional testing was required to rule out any substances that were administered in the hospital.
Hours later, a statement shared with PA on behalf of her family said the actress was being temporarily kept on life support.
"We want to thank everyone for their kind wishes and prayers for Anne's recovery and thank the dedicated staff and wonderful nurses that cared for Anne at the Grossman Burn Center at West Hills hospital," the statement read.
"Unfortunately, due to her accident, Anne Heche suffered a severe anoxic brain injury and remains in a coma, in critical condition. She is not expected to survive," the statement read.
"It has long been her choice to donate her organs and she is being kept on life support to determine if any are viable.
The statement added: "Anne had a huge heart and touched everyone she met with her generous spirit.
"More than her extraordinary talent, she saw spreading kindness and joy as her life's work - especially moving the needle for acceptance of who you love.
"She will be remembered for her courageous honesty and dearly missed for her light."
Heche is the former partner of US talk-show host Ellen DeGeneres - the pair began dating in 1997 before separating in 2000 - and is known for films including Donnie Brasco, Cedar Rapids and the 1998 Psycho remake.
Pictures and video footage obtained by US media outlet TMZ following the incident showed Heche driving a blue Mini Cooper, which was later pictured severely damaged at the scene.
The vehicle struck a two-storey home and "erupted in heavy fire" according to the Los Angeles Fire Department.
Almost 60 firefighters took 65 minutes to access, confine and fully extinguish the stubborn flames within the heavily damaged structure, according to an LAFD report.
Heche sustained a "significant pulmonary injury requiring mechanical ventilation" and "burns that require surgical intervention", a spokeswoman for the actress previously confirmed to PA.
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