According to the Daily Mail, police were using water cannons on board the ship in an attempt to get the group to leave.
"A demonstration in Calais has drawn around 2000 people and in the end around 200 people entered the port, with approximately 50 of them boarding a ferry, the Spirit of Britain, on an external deck," deputy Calais prefect Denis Gaudin told Reuters on Saturday.
Video: Hundreds of migrants & refugees break into #Calais port & make it onto UK passenger ferry #refugeecrisis pic.twitter.com/KkdsdcsShL— Phil Caller (@Phil_Caller) January 23, 2016
A spokeswoman for P&O Ferries said the port of Calais was still closed on Saturday evening.
She said the migrants had not managed to get inside the ship, as staff had locked the doors to prevent all access from the deck.
Thousands of refugees fleeing war and poverty in Africa and the Middle East have gathered over the past year in a vast slum near Calais, dubbed "the jungle", using it as a stopover point before trying to smuggle their way across to Britain in the hope of a better life.