Police attended an address in Dexter Way in the city at 4.50am after the ambulance service reported that two people had been seriously injured.
A 31-year-old woman named locally as Laura Boon and her 11-year-old daughter Ella were declared dead at the scene a short time later.
Family members and the coroner have been informed.
A 28-year-old man was later arrested on suspicion of the murder.
He is still being questioned by officers.
Cordons remain in place at the address and nearby boating lake (Westgate Park) while the investigation is ongoing.
Forensic enquiries will be continuing tonight and tomorrow and post mortem examinations are due to take place in the coming days.