Janet Llewellyn, 66, was playing on a nine-hole course with Ronnie Battersby when she was hit in the back of the head by his tee shot, it is understood.
The widowed mother-of-two collapsed immediately after being struck by Mr Battersby’s drive on the 271-yard par four third hole.
She was helped from the course by staff using a golf buggy and flown by air ambulance to the Southern General Hospital in Glasgow.