The suspect either fell or jumped from a balcony on the fourth floor of the building in which the body of the student was found.
The man broke several bones in the fall and is still being treated in hospital.
Prosecutor Anders Brokelind hopes that the suspect will be ready for extensive questioning at some point on Tuesday.
He would not say how the woman had died.
“She was a victim of violence but I would rather ot reveal the kind of violence involved,” said Brokelind.
The 22-year-old man is the only suspect currently under investigation.
“We are assuming that he was the perpetrator, at least to the point that one can assume anything at this early stage,” said Brokelind.