Two of the girls, all 15 years old, were being treated in hospital in the Azeri capital, with one of them, Vanessa Sahinovic, having sustained serious injuries.
Luna Pajer sustained an arm injury which will require further tests in Vienna.
Both will be flown back to the Austrian capital as soon as possible, while the third, Verena Breit suffered only a minor knock on the thigh and returned to the team quarters after a brief treatment.
USA's Artistic Swimming performance at London 2012
"Vanessa Sahinovic is unfortunately seriously injured, she suffered multiple injuries with several fractures," said Austrian team doctor Alfred Engel in a statement.
The incident occurred on Thursday morning with the three women walking on the pavement in the sprawling athletes' village when the bus hit them, according to the Austrian team.
The European Games start on Friday and run until June 28.
"We are shocked by this incident and have taken all necessary measures," said Austrian Olympic Committee general secretary Peter Mennel.
Russia’s near-perfect synchronised swimming routine at London 2012
Russia's prayer is answered with fifth synchro team gold