A passerby had discovered the newborn on Monday after descending into the drain, Garrith Jamieson, chief of Durban Rescue Care, said in a CNN statement.
Rescue teams broke chisel and hammer into the drain, Jamieson said. The whole operation took almost four hours.
After the baby was found and released, it was flown to the Inkosi Albert Luthuli Hospital for urgent treatment.
It was assumed that the baby, in which the umbilical cord was intact, was between one and three days old.
It was named by the residents Sibanisethu (Our Ray of Light) and Gabriella, the statement said.
"It's really a miracle that this baby was rescued, and the doctors have given this baby a clean bill and it's being moved to another hospital," said Regional Health Commissioner. Sibongiseni Dhlomo.