Emergency services were called to a house in Falmouth just after 08:00 BST.
The woman was taken by air ambulance to Derriford Hospital in Plymouth, where her condition was described as "stable".
Devon and Cornwall Police said a 77-year-old man had been arrested on suspicion of causing grievous bodily harm, and was being held in custody.
A woman in her 70s has been airlifted to hospital after being injured in a knife attack.