Carnival Cruise Line said in a statement that the Carnival Glory was maneuvering in the port when it "made contact" with the Carnival Legend in the morning.
Videos shot by startled passengers and posted on social media showed the noisy, slow-moving accident, which left part of the Glory visibly mangled at the stern.
The cruise line said it was assessing the damage, but there were "no issues that impact the seaworthiness of either ship." It said six guests came to the Glory's medical center for evaluation for minor injuries.
According to Carnival's website, the Glory sails from New Orleans on cruises to the Caribbean and the Panama Canal and is 952 feet long with a guest capacity of 2,980.
The Legend operates from multiple ports in the United States and Europe to a variety of destinations and is 963 feet long with a capacity of 2,124.