Officers were called to a home in Baulkham Hills, in the city's north-west, about 3.20pm (AEDT) yesterday where they found an injured woman.
"Police were called to a home in Cross Street ... regarding a domestic incident," NSW Police Force says in a statement today.
"Upon arriving, officers located a 46-year-old woman suffering wounds to her head."
Police say the woman was taken to Westmead Hospital in a critical condition, while the man was arrested at the scene.
He was taken to Castle Hill Police Station and charged with attempted murder.
The man was refused police bail and he is expected to appear in Parramatta Local Court today.