Amy Stringfellow, who was in her 20s, was found critically injured at a house in Dryden Road, Balby, on Friday, June 5.
Emergency services were called at 11.35pm but Amy could not be saved and was pronounced dead a short time later.
A 45-year-old man was arrested on suspicion of murder overnight on Friday into Saturday and remained in police custody last night.
An update on the progress of the investigation is expected from South Yorkshire Police today.
Detectives investigating the death of the personal trainer have urged anyone with information which could help them to come forward.
The house where Amy died was sealed off yesterday while crime scene investigators examined it and police officers carried out enquiries in the street.
Call 101 and quote incident number 904 of June 5.