Officers from West Yorkshire Police found the bodies of the woman, aged 31, and the girl, aged eight, in a property on Kirkby Avenue, Garforth, Leeds, yesterday.
Officers also found a four-year-old girl with minor injuries, a force spokesman said.
She was treated at Leeds General Infirmary and later discharged.
A 36-year-old was arrested on suspicion of murder and attempted murder and is being held in custody.
A force spokeswoman said: “Police were called around 4pm to reports of an assault near the Fairburnings Nature Reserve near Castleford.
“Officers attended and following initial inquiries a house search was subsequently conducted at an address in Kirkby Avenue in Garforth in Leeds and a 31-year-old woman and an eight-year-old girl were found deceased in the property.
“A four-year-old girl was also found with minor injuries.
“She was taken to Leeds General Infirmary and later discharged.
“A 36-year-old man was arrested on suspicion of murder and attempted murder.”