There are conflicting reports about the causes of the plane crash.
The South Supreme Airlines was coming into land after flying from the capital, Juba.
State governor Andrea Mayar Achor told BBC Focus on Africa radio that there were visibility problems.
But a journalist for Eye Radio said that "the plane was blowing smoke from the tail before it crashed".
The number of casualties is also not clear. There were at least 40 people on board, but some are said to have survived.
Eye Radio quotes the Director of Wau Teaching Hospital, Dr Edmond Sebit, as saying that several of the injured have been taken to the hospital.
South Supreme Airlines are not reporting any deaths at this stage, a local journalist told the BBC.
People are tweeting pictures from the scene.
Posted by Amare Asrat