The victim was found with serious stab wounds inside a house on Sutton Approach, off York Road in Killingbeck, on Tuesday night.
The male suspect is still at large.
West Yorkshire Police said:
"At 11:42pm last night, police were called to an address in Sutton Approach where a woman was found with serious knife injuries after being assaulted.
"The 38-year-old woman was taken to hospital for emergency treatment. Her injuries are not considered life-threatening and she remains in hospital.
"The incident is being treated as domestic-related and a suspect has been identified. Enquiries to locate and arrest him are ongoing."