The victim was taken to hospital by ambulance with a number of facial and hand wounds.
The incident happened at around 9.30am at Nicholas Street.
Both women come from the St Mary’s Park area and the attack was not linked to any gangland group.
One witness said: “The woman who was attacked ran up the street and was bleeding from the face and hands.
“Some people came to herassistance and others went to look after the child in the buggy.”
After being treated at the Mid-Western Regional Hospital, the injured woman was allowed home.
It is believed that a man was present when the attack was carried out.
Both woman are in their 30s and know each other, according to local sources.
Superintendent Frank O’Brien said no formal complaint had been made, so far, but gardaí will be following up the incident.
He said: “Gardaí responded to a call and it is being investigated. Anything like this is viewed seriously.”