It was unclear however if the rest of the those on board were alive or dead.
"There were 40 passengers and five crew (on board) that is all. I don't have any information," said Gabriel Ngang, the manager of South Supreme Airlines, the owner of the plane.
He said the jet had taken off from the capital Juba.
"Right now we have the ambulance which has just come out from the airport and we have received 14 patients being rushed to hospital in stable condition," said State Information Minister Bona Gaudensio.
Paul Charles, an engineer at Wau airport. said the weather in the region was not good.
"Visibility was not good up to now and (the plane) was landing from the east to west, then it just crashed (off) the runway. The pilot I think was not seeing the runway well," he said.
Images circulating on social media showed thick black smoke billowing from the aircraft, which was completely burned out except for the tail, which clearly displayed the insignia of local carrier South Supreme Airlines.
In November 2015, 36 people were killed when a Soviet-era Antonov plane crashed just after take-off from Juba. Two survivors were pulled out of the twisted metal hulk but one later died.
The plane crash is the latest tragedy to befall South Sudan, which has been gripped by civil war since 2013. The country is also in the midst of a "man-made" famine due to the conflict.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)