A man remains in a critical condition in hospital after being stabbed during an alleged domestic dispute at a home in south Sydney.

A 27-year-old man and a 21-year-old woman, who were in a relationship, were arguing at a home in Carlton on Wednesday morning before the man was attacked, police say.

The man was taken to St George hospital with stab wounds while the woman was arrested at the home and taken to Kogarah Police station where she was charged with wound with intent to murder.

She has been refused bail to appear in Sutherland Local Court on Thursday.