The blockade is a protest by the refugees, who say they want access to British officials so they can seek asylum in the United Kingdom, The Guardian reported.
Most of the protesters are men, about 20 who are on a hunger strike. Seven minors and a few women, one pregnant, are among the refugees.
A local official offered to allow the Syrians to apply for asylum in France, but they continued their protest.
When police arrived, two male refugees climbed to the roof and threatened to jump.
"More and more Syrians are arriving in Calais wanting to reach the U.K.," said Philippe Wanneson, a member of a French association that helps refugees in Calais. "A year ago we saw perhaps only two, three or four. Since March or April it has been rising to 20, 30, 40 and steadily growing."
A 24-year-old refugee who didn't want to give his name said it took him four months to travel to Calais from Turkey.
He described conditions in France as "very bad," with police arresting or following refugees.
"We don't hold any hope from the French government," the man added. "We hope that the British government will show some of the humanity it is famous for."
The protest is the responsibility of France, British authorities said.