"Vanessa Sahinovic suffered many fractures and more surgery will be necessary," hospital spokesman Christoph Mierau said, adding the 15-year-old Austrian's injuries were not life-threatening.
Sahinovic and two teammates - Luna Pajer and Verena Breit - were hit by the shuttle bus while walking on the sidewalk of the athletes village in Baku on Thursday. Pajer suffered a broken elbow and Breit escaped with bruises.
Video posted online shows the large bus taking a tight corner at a fast speed before veering onto the sidewalk and hitting the girls. One of the girls was dragged for several meters underneath the vehicle.
"The long-term impact is still difficult to tell. You need a week for that, in order to be really precise," Austrian team spokesman Wolfgang Eichler said of Sahinovic. "The spine has been severely damaged."
Sahinovic and Pajer were flown back to Austria hours after the incident. Pajer was expected to be released from the hospital soon.
According to the head physician of the Austrian Olympic Committee, Alfred Engel, all three girls received "very good" first aid at a hospital in Baku.
Authorities in Azerbaijan and local organizers of the games have started an investigation into the incident, which happened at 8:30 a.m. Thursday.
"We'll be kept updated about what measures are taken," Azerbaijani Sports Minister Azad Rahimov said.
Rahimov added he received information that Sahinovic "moved her legs. We were frightened it would be something much worse."
The Vienna hospital, however, gave no indication of Sahinovic's recovery prognosis.
On Friday, two of the injured girls' teammates took to the water, with sisters Anna-Maria and Eirini-Maria Alexandri finishing fourth in the preliminary round of the duet competition.
"Taking into account the circumstances, this was an unbelievably strong achievement from the pair, who definitely wanted to compete for their injured teammates," Austrian Olympic Committee president Karl Stoss said in a statement.
AP Sports Writer James Ellingworth in Baku, Azerbaijan, contributed to this report.