Vanessa Sahinovic, 15, was one of three Austrian swimmers injured as she walked along the pavement in the village on Thursday. She was flown back to Vienna the same day.
"The 15-year-old suffered multiple fractures and was flown to Vienna where she was operated on all night," the Austrian Olympic Committee (AOC) said in a statement.
"Apart from her hip region and thigh, her spine has also been affected," it said.
"Sahinovic is at the moment in an artificial deep sleep and will undergo more operations in the coming days."
Games organisers said police have launched an investigation into the accident.
Team mate Luna Pajer, who was also flown back, broke her arm and will be released from hospital soon while Verena Breit received treatment in Baku and returned to the team.
"We are still all in a state of shock," AOC President Karl Stoss said.
"It is difficult to comprehend that his accident happened without any involvement of the girls who were walking on the pavement in the athletes' village."
The European Games officially start later on Friday and run until June 28.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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