The incident at a South Rd house was reported to emergency services about noon yesterday.
Detective Senior Sergeant Kallum Croudis, of Dunedin, declined to give details of the woman's injuries or her male attacker yesterday, but said police knew for whom they were looking.
The suspect left the scene of the attack with a young child, but police later found the child safe and well, he said.
The armed offenders squad was called in as police mounted a search for the man.
Squad members in three police cars were parked in Brockville Rd, near Turnbull St, yesterday afternoon.
One witness, who contacted the Otago Daily Times, said it was an "exciting spectacle" as police cars "frantically" drove and reversed up the street with AOS members in black clothing loading weapons.
The AOS was later stood down but police continued to search for the man.
"There is no reason to believe he is a risk to anyone else," Det Snr Sgt Croudis said late last night.
The woman involved was still in a serious condition in hospital.
"That is of significant concern to us but she is in the best place for her now," he said.
Further details of the incident may be released today, depending on the progress of the investigation, he said.
It was the second serious incident in Dunedin during the weekend.
On Saturday, a man and a woman were attacked in Fawcett St, St Kilda. Both suffered injuries. Two men had been arrested in relation to that incident.
