Officers were called to an address on Walpole Road, Huddersfield, West Yorkshire, at about 8am on Monday, after they received a report of concern from the ambulance service.
They found three young children - two boys and a girl - and a woman, with serious injuries, believed to have been caused by a bladed weapon.
All four were taken to hospital and are being treated for those injuries, West Yorkshire Police said.
A woman has been arrested on suspicion of attempted murder as part of the investigation.
Detective Chief Inspector Sam Freeman, of the homicide and major enquiry team (HMET, said: “Inquiries are ongoing today into what has clearly been a serious and distressing incident in Huddersfield and we fully appreciate the concern it will cause in the local community.
“Detectives are conducting inquiries to determine the exact circumstances of what has taken place and an arrest has now been made as part of those investigations.”
Chief Inspector Rebecca Calpin, of Kirklees Police, said: “Reassurance patrols are taking place in the local area by officers from the Huddersfield neighbourhood policing team and will be continuing throughout the day as Kirklees officers work to support colleagues from HMET.”
