Officers were called to a property in Churchill Place, Brooke, at around 10.30am on Sunday to reports a woman had been stabbed.
They discovered the body of a woman, who was pronounce dead at the scene.
Police have not released the woman’s age or identity.
The suspect was detained at the Norfolk and Norwich University Hospital, according to the Eastern Daily Press.
Detective Inspector Chris Burgess said the man and woman are believed to have know each other.
He said: “Clearly we are still in the early stages of our investigation and our enquiries remain ongoing.
“We do not believe there to be any threat to the wider public.”
A cordon has been put in place outside the property while officers continue their enquiries.
:: Anyone with information is asked to call police on 101.