Dr Donald MacKay, 56, was attacked by a man who smashed his way through a security door and confronted him in the Bankhouse Medical Centre in Airdrie, near Glasgow. Police said they did not yet know the motive of the attack.
After an altercation the man stabbed Dr MacKay, who lived in Airdrie. He died despite the efforts of people in the surgery, including his daughter Laura, who works there as a receptionist, to save him.
The killer ran from the health centre towards some nearby flats. Detectives are looking for a man in his mid thirties with dark shoulder-length curly hair, wearing a dark jacket and blue jeans.
They are also checking film from a town-centre security camera about 100 yards from the surgery to see if the intruder was filmed. The murder weapon, described by police as a 'sharp instrument', was found nearby.
A BMA spokesman said last night: 'We are very concerned about the overall problem of violence against doctors. With the increased expectations that patients have from their doctors, attacks and physical confrontations have become more common.'