"A group of 500 people forced their way through police lines and headed to the port, and 150 people were able to get into the fenced-off area. Of these, a group of some 50 managed to board a ferry," police said.
The port issued a statement that the estimated 30-40 migrants who boarded the Spirit of Britain ferry, operated by P&O, were calmly removed by police around two hours and the port reopened around 8.30pm local time.
Earlier in the day demonstrators hailing from Britain, France, Belgium and Italy held banners reading "Refugees welcome", "Calais, Lesbos, Lampedusa, our borders kill", "Open the borders, let them in".
Port director Jean-Marc Puissesseau called for the Jungle to be relocated.
"The proximity of the camp and the unprecedented number of migrants make it impossible to secure the (port) infrastructure, however much the state invests," he told the AFP news agency.
British opposition leader Jeremy Corbyn on Saturday visited the neighbouring town of Dunkirk, which is home to another camp named the Grande Synthe.
Corbyn, a veteran left-wing campaigner before becoming Labour leader, said he wanted to "understand the nature of the refugee crisis that's facing the whole of Europe".
He said that Britain should do more to address the problem.
"These conditions are a disgrace anywhere. We as human beings have to reach out to fellow human beings." he said.