Police in the Pas-de-Calais department where the port is located said they had to call in reinforcements to deal with the asylum seekers.
"Some 300 to 400 migrants wanted to climb aboard the trucks and the CRS (riot police) had to use tear gas to disperse them," a police souce said.
The line of trucks waiting to board ferries bound for Britain was longer than usual, and some migrants likely slipped into some of them unnoticed, the source added.
The port is struggling to stem a tide of illegal migrants trying to cross the Channel to Britain, which they see as having a favourable asylum policy, despite a slew of recent measures to tighten security.
The problem in Calais is not new — illegal camps of migrants have sprung up in the area since French authorities closed down the infamous Sangatte immigrant detention centre in 2002.
French Interior Minister Bernard Cazeneuve said last month that Britain had agreed to contribute up to €15 million (£12 million, $19 million) to a fund to help deal with the problem after Calais's mayor threatened to close the busy cross-Channel port.
France had long called on Britain to help pay for security measures at the port, where police say up to 1,500 migrants, mostly from Sudan and Eritrea, are trying to slip into trucks bound for Dover.