The 30-year-old had picked up two men and a woman in Hamilton Road, Cambuslang, and taken them to an address in Altyre Street at 02:00.
At the address one of the men produced a knife.
The taxi driver got out of the car, at which point a group of people came out of a property. They surrounded him before attacking him.
The group then went back inside the property.
The victim got back into his taxi and drove a short distance before stopping and calling an ambulance.
He was taken to the Glasgow Royal Infirmary for treatment to a stab wound. Medical staff have described his condition as stable.
The first male passenger is described as short, in his late 20's, of medium build and spoke with a Glasgow accent. The other male passenger also had a Glasgow accent.
Police described the female passenger as being about 5ft 4in and of slim build. They also said the trio were involved in the assault.
Det Insp Tom McKean said: "Why a group of people would target an innocent man in this brutal fashion is beyond me and we are currently working to establish the motive for this horrendous incident.
"This type of behaviour is disgraceful and simply will not be tolerated and our officers will do everything they can to find the people responsible for this despicable crime.
"I would appeal to anyone who was in Altyre Street or the surrounding area in the early hours of this morning, who may have witnessed a disturbance or saw anything suspicious, to get in touch."
A taxi driver has been stabbed in an attack by a group of men and woman who tried to rob him in Glasgow.