There are six minor injuries reported, which Donald said occurred as "people tried to leave the dining room."
"Everyone is all right," Donald said on "Closing Bell."
"We will do a deep investigation on this," Donald said, adding the company takes seriously its responsibility for safety. "But the most important thing is the ships are able to sail and they can continue on with guests having a great vacation."
People who have booked future trips on either ship involved — the Carnival Glory and the Carnival Legend — will be able to go on them as planned. The Glory has some damage, but it will be repaired shortly, Donald said.
Donald said the collision likely happened due to a "sudden squall ... of wind that pushed the ships."
"Occasionally ships will touch in port, but of course you try to avoid that," he said.
News of the ship accident comes as Carnival reported better-than-expected quarterly revenue Friday, boosted by higher on-board spending.
Shares of the world's largest cruise operator were up more than 7% Friday, concluding the session at $50.21. That is about $9 off its 52-week high in February.