Dr Antonella Castelvedere, 52, has been named in Italian media as the woman who died at an address in Wickham Road in Colchester, Essex.
Essex Police said officers were called to concerns for the welfare of a woman at the address shortly after 11.45am on Wednesday June 1.
Officers found a woman who was seriously injured and she later died at the scene.
The force said officers also found a man injured at the address, and he was arrested on suspicion of murder and taken to hospital for treatment.
Police have not named the deceased woman, but the University of Suffolk said in a statement: “The University of Suffolk community is deeply saddened by the untimely death of Dr Antonella Castelvedere.
“Antonella was a widely respected and well-liked member of staff at the University where she was an outstanding academic in English and Critical Writing.
“Our thoughts are with her family at this very difficult time.”
Detective Chief Inspector Antony Alcock, of the Kent and Essex Serious Crime Directorate, who is leading the investigation, said detectives were “continuing to piece together the circumstances which led up to this incident”.
He said inquiries “suggest this was an isolated incident and there is no threat posed to the wider public in Colchester”.