In the pioneering procedure, carried out in northern France on Sunday, a triangular section taken from a dead donor's face, including the nose, mouth and chin, was transplanted onto the patient.
The medical team included Professor Jean-Michel Dubernard, a leading French surgeon who performed the world's first hand transplant in 1998.
"At this point, the patient is in excellent general condition and the appearance of the transplant is normal," the two hospitals involved in the operation said in a statement.
The patient from the northern French town of Valenciennes was admitted to hospital in May with severe, disabling facial injuries after being mauled by a dog.
Facial transplant surgery, which carried high physical and psychological risks, was essential to restoring the functions she lost after her accident, the hospital statement said.
"Beyond its aesthetic consequences, the injury provoked lesions that turned out to be severely disabling both for speech and for the chewing function," the statement said.
Such injuries were "extremely difficult, even impossible to repair using conventional oral-facial surgery techniques," it said.
The transplant was carried out by a team led by Professor Bernard Devauchelle, an oral-facial specialist, at the university hospital in the northern French town of Amiens, the statement said.
Earlier Sunday, the facial tissues, muscles, arteries and blood veins needed for the transplant were taken from a donor in a brain-dead condition, whose family had authorised the procedure to go ahead.
The patient will have to take immuno-suppressant drugs to prevent her body from rejecting the donated tissue and will remain under Dr Dubernard's supervision at the university hospital in the central-eastern city of Lyon.
A French professor, Laurent Lantieri, who was working towards carrying out a facial transplant, said: "We should know by the end of the week whether it has held, if there has been no full-scale rejection".
Computer modelling suggests the patient's new face will eventually be a hybrid of her own and that of the donor.
The transplant procedure could bring hope for thousands of people whose faces are disfigured by burns, trauma, disease or birth defects, although ethical concerns have held back its development in many countries.
Until now, surgeons have used skin from patients' backs, buttocks or thighs for grafting onto their faces, but the result is often mask-like and recipients regain limited facial function, even after dozens of operations.
The French news magazine Le Point said French health authorities gave the go-ahead for the operation in August.
Dr Dubernard, a surgeon at the Edouard Herriot university hospital in Lyon and a French deputy, performed the world's first hand transplant in September 1998, followed by the first double hand and forearm transplant in January 2000.