The girl is being treated at the city's teaching hospital and is able to recognise relatives, journalist Philip Mabior from Juba's Eye Radio reports.
At least 36 people died after the plane crashed on take-off near Juba airport.
The cause of the crash remains unclear but the manufacturer said the cargo plane was not airworthy.
The UN peacekeeping mission in South Sudan has sent divers to search the nearby White Nile for bodies, and also for the black box recorders.
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.
The cargo plane was not authorised to take passengers, Stephen Warikozi, the head of South Sudan's Civil Aviation Authority told journalists, but there were thought to have been dozens on board. They were all from South Sudan.
It is not clear what caused the crash but Ukraine-based Antonov said the plane had not been airworthy.
Five of the six crew members were Armenian, while the sixth was Russian. They were all killed.
A 14-month old girl who survived Wednesday's plane crash in South Sudan's capital, Juba, is now conscious, doctors say.