A spokeswoman said some "small guide wheels" came off The Smiler as it was being pulled up an incline.
Kevin Hayes-Heath, who was in the carriage with his partner Wayne, said the incident was "pretty frightening".
Debris hit him on the shoulder and his partner in the face. A teenage girl and her father were also hit, he said.
"You are at the highest point of the ride and you've got all these loops to do and you just think that the carriage is going to come off," Mr Hayes-Heath said.
"We were shouting at them to stop the ride because they were about to send another party off."
Alton Towers said the ride completed its circuit and no evacuation was required.
A spokeswoman confirmed that plastic guide wheels were flicked onto a teenager and three adults in the front row of the train.
The rest of the guide wheels were caught by safety netting, she added.
The injured people were looked after by park staff and did not need treatment by the ambulance service, the spokeswoman said.
The park said an investigation would be carried out into Saturday's incident to decide when the ride could re-open.
It looks like instead of "The smiler" it should have perhaps been called "The Lemon"....
Walt Disney World
Tokyo Disney Resort