An inspection by the U.S. Centres for Disease Control (CDC) when it docked in Baltimore also revealed eight of the crew had fallen ill.
A cruise on the same ship was cut short last year when passengers suffered a "gastroenteritis-type" illness.
In response to the latest outbreak, Fred Olsen Cruises said it had increased cleaning and disinfection procedures, collected specimens for testing and was making daily reports of cases to the CDC`s Vessel Sanitation Programme.
The Balmoral is on a 34-day "Old England to New England" cruise and is currently sailing to Saint John, in the Canadian province of New Brunswick.
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