Police said it happened near a garden centre at Rogers Farm on the A24 near Findon, West Sussex.
The 79-year-old victim died at the scene, at about 20:40 BST on Thursday. A murder investigation is under way.
The suspect, described as a tall, skinny, white man in his 30s, is thought to have been driving the car in front of the man who was stabbed.
The attacker is said to have shoulder-length, wavy brown hair and was thought to be driving a pale "old-style" car.
It is believed the victim was travelling alone and that he was stabbed more than once.
Det Ch Insp Karen Mizzi said: "Officers have been urgently making inquiries overnight to trace the suspect.
"We need to hear from witnesses who saw the collision, the suspect or the car involved, particularly if anyone filmed the incident or saw anyone filming it."
Laura Muchmore, 21, who works in the garden centre close to the scene of the stabbing, said: "It's especially shocking that the victim was an old man.
"Findon is a really lovely little village. It's so picturesque and it's not known for this type of crime."
Edmund King, president of the AA, described it as a "horrific and tragic incident".
He said: "Thankfully, such brutal 'road rage' attacks are generally a rare occurrence on our highways.
"It appears that some drivers do react differently when they are behind the wheel than they would if they were walking down the street.
"They almost feel that the car empowers them but in reality it does not."
A manhunt is under way for a driver who stabbed another motorist to death after a collision between their two cars.