"Diverted flights have also been cleared to land at the JKIA as the temporary shutdown has been lifted."
In the statement, KQ spokesperson Dennis Kashero said they were notified of a possible bomb threat at about 1.15pm.
The plane was headed for OR-Tambo International Airport in the South African city.
“KQ would like to report that the passenger who raised the bomb scare has been taken into police custody,” Mr Kashero said, without revealing the person's identity.
The passenger was handed over to the Anti-Terror Police Unit for interrogation.
The airline re-screened passengers and carried out extensive security checks after the incident as part of precautionary measures.