The child was discovered seriously wounded at a property in Brownhills, near Walsall, on Saturday night, and died a short time later in hospital.
West Midlands Police said the man, 54, was also taken to hospital with a stab wound to the stomach.
He is in a stable condition and will be questioned "in due course" over the incident in Valley View, a residential street on the edge of the town.
Police were called to the scene at 9.15pm.
Detective Inspector Jim Colclough, from the homicide unit, said: "We are treating this as a domestic incident and are not looking for anyone else in connection with the child's death.
"Our family liaison team are supporting the family of the little girl, who are naturally devastated by her death. Our thoughts remain with them."