The Antonov An-12 plane, operated by local company Allied Services Limited was heading to Paloch, Upper Nile State, and came down 800m (half a mile) from the runway.
It crashed into a farming community on an island on the White Nile, but it is not clear how many of the victims and survivors were passengers and how many were on the ground.
It is not clear if the 14-month old girl is the only survivor.
She was one of two people taken alive from the wreckage on Wednesday, the other is reported to have died later.
However, Philip Mabior said another person who survived the crash was also being treated in hospital.