Police were called to an address at the Saxton flats development in the Richmond Hill area of the city shortly before 9am yesterday.
A woman was pronounced dead at the scene. She is thought to have been in her 20s.
The man arrested in connection with the incident was today in custody. He is aged 25.
A spokesman for West Yorkshire Police said: “A scene is in place at the address and enquiries are ongoing.
“This incident is believed to be domestic related and police are not looking for anyone else in connection with it.”