Since he was hit by a massive stroke on 4 January, Sharon has been in a coma. Experts in long-term care and a U.S. authority on comatose patients have examined Sharon in recent days.
Experts say his chances of regaining consciousness, or a meaningful level of activity are slim.
A statement from Jerusalem's Hadassah Hospital, where Sharon is being treated, said the operation was successful, and was carried out under anesthetic.
The statement said Sharon's condition continues to be critical but stable.