On 19 September 1988, Kinnear fell from a horse during the making of The Return of the Musketeers in Toledo, Spain, and sustained a broken pelvis. He was taken to hospital in Madrid but died from a heart attack the next day. He was 54 years old. He is buried in East Sheen Cemetery.
After his death, Kinnear's family demanded an official investigation into the level of medical care he had received in Spain. Director Richard Lester decided to quit the film business as a direct result of Kinnear's death.