Most of the sick have vomited and have diarrhea, reports the US disease control authority CDC.
The outbreak was reported according to CNN when the ship was approaching the end of a four-week long round trip from the UK to the Caribbean. The sick have been isolated and the ship will now be cleaned and disinfected, announces the shipping company Cunard Line.
Norovirus is sometimes called the "cruise virus" as it spreads quickly in enclosed spaces, such as cruise ships. Virus particles can survive for days or even weeks.
Queen Mary 2, which claims to take passengers back to the "golden era" of ocean travel, sailed from Southampton on March 8 and is expected to return to the British port on Sunday.