The alleged fight took place as P&O's Britannia returned to Southampton from a week-long trip to Norway's fjords.
Good Morning Britain journalist Richard Gaisford, who was on board, said the violence occurred after a black-tie evening and an afternoon of "patriotic" partying on deck, when large amounts of alcohol were consumed.
He said one witness "explained to staff that things kicked off when another passenger appeared dressed as a clown. This upset one of their party because they'd specifically booked a cruise with no fancy dress. It led to a violent confrontation."
The people suspected of being behind the violence were confined to a cabin for the last day of the cruise.
A P&O Cruises spokesman said: "Following an incident on board Britannia on Thursday evening we can confirm that all guests have now disembarked and the matter is now in the hands of the local police."
Hampshire Police said its officers attended the ship when it docked in Southampton and investigations are ongoing.
The mere presence of clowns does affect some people negatively .....