Norwegian Cruise Lines says the Norwegian Escape ran into winds estimated at 115 mph (185 kph) late Sunday that caused the ship to tilt to its port side.
The cruise line said in a statement Tuesday that several injuries were reported, but it didn't say exactly how many or what type of injuries occurred.
Norwegian says the passengers received treatment from medical staff. The ship had no damage and remained fully operational.
The ship was on a seven-day round-trip cruise from New York to Florida. It arrived at Port Canaveral, Florida on Tuesday.
The ship can hold more than 4,200 passengers and more than 1,700 crew members.
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