The overloaded commercial plane crashed into a lake in Yirol.
The 19-seater commercial Baby Air plane had been travelling from the capital, Juba, the minister of information for the town of Yirol, Taban Abel Aguek, told The Associated Press.
Officials are investigating the cause of the crash.
According to the Anglican Communoin News Service, the Primate of South Sudan, Archbishop Justin Badi Arama, said: "Mama Joyce and I are saddened to hear of the plane crash in Yirol this morning, which has claimed the lives of a number of people, including the ECSS Bishop of Yirol, Rt Revd Simon Adut Yuang.
"Bishop Simon was an energetic young man and is a loss to the Episcopal Church of South Sudan. Please join us in praying for the families and friends of all involved in the accident.
"Jesus said, 'I am the resurrection and the life. The one who believes in me will live, even though they die."
The three survivors of the crash are a six-year-old child, an adult man and an Italian doctor with an aid organisation who was in surgery and in serious condition, Mr Aguek said.
"There were people everywhere," the minister said of the crash site.
Bishop Simon was consecrated in May 2015. He leaves behind a wife and six children.
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