Family launch crowd-funding campaign to bring the rower home, who has been focusing on getting in the British team for the Tokyo Olympics in 2020.
Team GB star Thornton, 21, was hurt in the fall earlier this month in Washington, US, and is said to be in a “stable but serious condition”.
The World Under-23s champion in the double scull, from Nottingham, is studying in Seattle.
In a statement, the University of Washington — where Thornton has a full scholarship and is studying public health — admitted their shock.
A spokesperson said: “We have been closely monitoring the condition of Anna Thornton, a member of the UW women’s rowing programme who is in a stable but serious condition with injuries resulting from an accident earlier this month.
“At this time our focus is on supporting her, her family and team-mates in any way possible.
“Anna’s family has requested for their privacy to be respected at this time.”
A crowd-founding page has now been set up to raise money to bring her home from the Seattle hospital. Her family are looking to raise £80,000.
Thornton, who has won five gold medals at junior and U23s level, took up rowing at the age of 12 at Nottingham Rowing Club and is targeting a spot in the 2020 Olympics.
She represented Team GB Juniors at the 2014 Youth Olympic Games in Nanjing, China.
Thornton, who is in her third year of university, said her proudest achievement so far was winning gold in the Women’s U23s quad.
In an interview with worldrowing.com, Thornton said: “I had won a bronze and silver at the World Rowing Junior Championships, then a silver at the U23s in Rotterdam and wanted the elusive gold medal at Plovdiv.
“My goal in rowing is to win some more World Championship medals and hopefully compete at the Olympics.”
She also said she wants to be invited to the GB senior team and train full-time when she finishes university.
Thornton’s nickname is ‘Thorndawg’, which she says is a “play on my last name, and our university mascot being the husky”.
A statement from British Rowing added: “At this time our focus is on supporting her and her family in any way possible.”