The woman - a Hungarian national aged 51 years - underwent emergency surgery at Cork University Hospital (CUH) after being found in a critical condition with stab injuries near her Banteer home in north Cork.
Gardaí believe the woman was involved in an argument with a person known to her shortly after 4pm on Christmas Day at the property just outside Kanturk.
She left her property and went to get her dog to take it for a walk.
However, she was apparently pursued by the male individual and then attacked.
During the attack, she was stabbed in the torso.
The alarm was raised by another woman who was shocked to discover the condition of the 51 year old.
The injured woman was rushed by ambulance to CUH where she was initially in a critical condition.
Doctors were able to stabilise her condition and she later underwent emergency surgery for the stab wounds to her chest.
Sources said Gardai are hopeful the woman will recover fully from her ordeal though she remains in a serious condition.
A major search was launched for the man involved in the confrontation.
Gardai supported by the Regional Armed Support Unit rushed to the scene.
A man in his late fifties was found by members of the Armed Support Unit a short distance from the house with several injuries shortly before 6pm.
He was also transferred by ambulance to CUH where he is also being treated for non life threatening injuries.
He remains at the hospital.
Gardai hope to speak with the female victim in the case once she is certified as being medically fit by doctors who are attending to her care in hospital.
Both the house and the area where the man was found were due to be forensically examined by members of the Garda Technical Bureau.
Gardai from multiple divisions, including Kanturk and Mallow, attended at the scene alongside the Armed Support Unit and an army search team from Collins Barracks in Cork.
Shortly after 4.30pm (on Saturday) gardai were called to the scene of an incident at a residence at Banteer near Kanturk, Co Cork, a garda spokesperson said.
"A woman (50s) was removed from the scene by Ambulance to CUH for treatment of apparent stab wounds. Her injuries are described as serious but not life threatening."
"A man also in his fifties was located near the scene a short time later. He has also been taken to hospital for medical treatment. The scene is preserved for examination. Gardai are not seeking anyone else in relation to this incident. Enquiries are ongoing."