Mr Hooper said the mother managed to fend off the assailant and flee with her daughter.
A passing motorist picked them up and took them to hospital.
The man was described as light-skinned, about 1.84m tall with short hair and facial stubble. He was wearing jeans and a black hoodie.
Mr Hooper said police were seeking information about any suspicious activity in the suburb of City Rise between 7am and 9am today.
"It may be that members of the community have noticed someone who matches the general description of the assailant, who was acting unusually or out of character either before or after this time.
"This is a very serious potentially life-threatening incident and police seek the assistance of the Dunedin community and wider public for any information that may assist this investigation,'' he said.
Police also asked people living in the area to search their properties and if they found any items that might not belong to them to report it to the police.