37 people had been treated for injuries in hospital but, miraculously, no one was killed.
"There is no one who died," Bona Gaudensio, information minister in the northwestern state of Wau where the accident happened, said on Tuesday.
He said 37 people had been treated for injuries in hospital but, miraculously, no one was killed, despite a fireball consuming the plane soon after it crash landed.
Wau is a regional capital with a busy airport used by the United Nations and aid agencies as well as private and commercial planes.
The carcasses of older air crashes lie in the long grass next to the runway.
"The plane hit a fire brigade truck, that is how it caught fire," said Gaudensio.
He suggested both "a technical problem" and "some negligence" might be to blame and added that an investigation would be carried out.
Bad weather has also been blamed for the accident.
Pascal Ladu of the South Sudan Red Cross said that after the plane operated by local carrier South Supreme Airlines hit the truck it burst into flames and "passengers quickly started running out".
Monday's crash threw a thick plume of black smoke into the sky while firefighters and UN peacekeepers worked to contain the fire.
In the end, all that remained of the plane was its tail, clearly marked with the South Supreme Airlines insignia.
The aircraft had taken off from the capital Juba for Wau on Monday afternoon, according to airline manager Gabriel Ngang.
"It was bad weather that caused the accident, and also the truck of the fire brigade parked at the airport because the plane hit the truck. It was not to be parked there so these are what caused the accident," he said.
Ngang said his airline, operating in South Sudan since 2005, has a fleet of 15 planes and operates flights both domestically and internationally to Sudan, Jordan and Syria.
There were conflicting accounts of the number of people aboard the plane, with Ngang giving a figure of 45 and Gaudensio quoting 49.