Five men and one woman in their 20s were detained at about 08:00 BST on Friday in the departure zone of the Kent port, police said on Twitter.
Searches have taken place at a number of addresses in Birmingham.
Police said the arrests were part of an on-going investigation, and the suspects are not a family group and were not accompanied by children.
Four of the men arrested are from Birmingham - a 25-year-old from Small Heath, two 26-year-olds from Acocks Green and Alum Rock and a 28-year-old from Lozells, police said.
A man aged 26 and a 23-year-old woman of no fixed address were also held.
The suspects are being questioned at a police station in the West Midlands area.
They did not pose any immediate risk to public safety, the force added.
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