A woman and a baby were killed in the accident.
Morton and his wife were on their honeymoon in South Africa.
The 58-year-old biographer and journalist, who became famous for his tell-all biography on the late Princess Diana, suffered broken ribs, while his wife Carolyn, 51, sustained a broken sternum.
The Citizen reports that the couple arrived in SA at the beginning of November and started their visit in Franschhoek.
The accident happened on a remote road near the Kruger National Park.
Andrew and his wife were on their way to the airport after their two-week honeymoon when the car they were travelling in collided with another vehicle.
The passengers of the other car, a woman and a two-month-old baby, died at the scene. Another passenger was also injured and was taken to Matikwane Hospital in Mpumalanga.
The Mortons' vehicle was driven by a local driver from Tamboti Tours, Johan Scholtz.
According to the article, Morton remembers colliding head-on with the "silver Honda" on a steep hill.
The Evening Standard newspaper spoke to Andrew Morton. "I am well under the circumstances," Morton told the newspaper. "The other people are dead. Had my wife and I not been wearing safety belts, we would have been dead."
He recalls the honeymoon as a "marvellous holiday".
"We were watching lions and a female leopard shortly before hitting the road and that horrible accident happened," he said.
Carolyn has since been discharged from the medical centre in Nelspruit they were sent to, but Andrew has been asked to remain for observation.