The line confirmed the incident happened at around 6am (UK time) as the 1,400-passenger vessel attempted to berth for the scheduled visit.
It added: “Despite the assistance of two tugs and a pilot, Ambience was unable to maintain position in strong, gusting winds and made contact with the container ship, which was already alongside.
“Both ships report only minor damage and there is no water ingress or pollution.”
No injuries have been reported and Ambience is now safely docked at the cruise passenger terminal in the South African city.