A University of Georgia student was seriously injured after falling out of the window of her 8th-floor apartment ... and now she's hospitalized.

According to the Athens-Clarke County Police Department ... the unnamed student was dancing on her couch Saturday when she ended up falling out of the open window.

Authorities say she landed in the courtyard and pool area of the Rambler Athens apartment complex, which is a popular off-campus housing complex.

Police say she was taken to a hospital nearby, where she's "conscious and alert but seriously injured."

The apartment complex's management team sent a note to residents after the incident, reminding them their windows are equipped with "safety limiters."

The email said ... "For your safety, please do not tamper with, remove or disengage these devices. If you have a concern with a window or safety limiter, please contact the management team for assistance."

It went on to say ... "Our thoughts are with the resident and their family, and we ask that everyone respect their privacy during this time."