Jeremy Corybn visited refugee and migrant camps in Calais, saying conditions would be a "disgrace anywhere"
The Port of Calais had to be temporarily closed after scores of refugees and migrants stormed on to a ship in the hope of reaching the UK.
About 50 people made their way on to a P&O-operated vessel called Spirit of Britain.
The company described it as a "security incident" and reported that its vessels were delayed by 90 to 120 minutes.
Police attended the breach, which lasted about four hours.
DFDS Seaways tweeted late on Saturday afternoon: "The Port of Calais has been temporarily closed due to a migrant invasion, as soon as they are cleared the Port will re-open."
The shut-down followed a protest march in support of the refugees and migrants that was reportedly attended by 2,000 people.
A statement from the Port of Dover during the disruption said: "The Port of Calais is currently experiencing migrant activity which has caused disruption to ferry services. Therefore services to and from Calais via the Port of Dover are affected, but DFDS Seaways services are still running to Dunkirk as normal.
"The Port of Dover remains open for business, but the duration of this disruption to services remains unknown."
The UK's Road Haulage Association has repeated its calls for the French military to intervene at the port.
Its chief executive Richard Burnett said: "This shocking breach of security clearly shows that the migrant mayhem in and around Calais is not being tackled.
"This latest episode has made the headlines, but the many incidents of attacks and intimidation faced by our British drivers on a daily basis are going unreported as, depressingly, they are now being regarded as routine."
Mr Burnett said immediate action was necessary, warning that it is "only a matter of time before our worst fears become a reality and a UK-bound truck driver is killed".
In August, the UK and France reached an agreement aimed at stopping security breaches and easing the migrant crisis.
The latest incident coincided with Jeremy Corybn's visit to the refugee and migrant camps in Calais and Dunkirk where thousands of people are sleeping rough - his first foreign trip as Britain's Labour party leader.
He said the conditions would be a "disgrace anywhere" - and that thousands of people were living in a "sea of mud".