A bystander had spotted the newborn after climbing down into the drain on Monday, Garrith Jamieson, head of Durban Rescue Care, said in a statement obtained by CNN.
Rescue services used a chisel and hammer to break into the drain, Jamieson said. The whole operation lasted nearly four hours.
After being located and extricated, the baby was flown to Inkosi Albert Luthuli Hospital for urgent care.
Dramatic video from the scene showed the moment the baby was lifted to safety.
The baby, who was found with her umbilical cord intact, was believed to be between one and three days old.
She was named Sibanisethu (Our Ray of Light) and Gabriella by residents, the statement said.
"It's really a miracle that this baby was saved. The doctors have given this baby a clean bill of health, and she will be transferred to another hospital," said regional health official Dr. Sibongiseni Dhlomo.