"Photos from the scene show fire engines dousing the smouldering wreckage with water".
Initial reports suggested as many as 44 people were on board when the passenger plane crashed at Wau Airport on Monday afternoon, though an official passenger list is not yet available.
Achieng said 25 people were taken to a hospital and 18 are safe and have gone back to their homes.
He said all of the passengers were evacuated from the plane before it was destroyed by the fire.
The flight was traveling to Wau from the South Sudanese capital, Juba, a local official told the BBC.More news: Son was 1 of 2 killed in 'Real Housewives' auto , mom says
Images appeared on social media of the plane with smoke billowing from the wrecked fuselage.
Gabriel Ngang, the manager of South Supreme Airlines, told AFP that 40 passengers and five crew were on board. Peacekeepers from Bangladesh, Nepal and China helped in the emergency work, he said. It was making a trip from Juba to Wau, in northwestern South Sudan when it crashed.
There was no immediate comment from the South Sudanese government.
Dozens of people have been killed in a plane crash in South Sudan.
More than 12 million people live in South Sudan.