"One patient has been evacuated ... Scores are feared trapped," the organisation said.
Transport Minister Joseph Kamau, who was at the scene, told journalists that six injured had so far been taken to hospital.
"The rescue efforts are underway, we cannot talk of the number of those injured at the moment," Nairobi Police chief Benson Kibue told AFP.
One of Africa's largest slums, Kibera's tin-roofed shacks are home to an estimated quarter of a million people, according to an NGO that carried out a population study there.
"We have always warned people against encroaching on the line," he said.