The cargo plane was carrying 19 people, 17 of whom died in the crash, Ateny Wek Ateny, press secretary in the South Sudan president's office, told CNN.
The survivors were a crew member and a child whose age is not known, Ateny said. Those on board included 15 South Sudanese passengers and four Russian crew members.
The cause of the crash might have been engine failure, Ateny said, although he cautioned this had not been confirmed. He said a witness saw one engine fail before the plane crashed.
Wreckage in the reeds
The Antonov crashed less than 100 yards from the White Nile at 9 a.m. local time (1 a.m. ET) Wednesday, the spokesman said. A photo published by one local news organization showed the charred wreckage of a plane in the reeds near the riverbank.
The plane was bound for the northern South Sudanese town of Paloich, in an area of oil fields.
South Sudan is the world's newest country, having gained independence from Sudan in 2011.
This is the second Russian plane to crash in the last four days. On Saturday, a Russian passenger plane went down in Egypt's Sinai desert, killing 224 people aboard. The cause of that crash has not been established.