Far-right and left-wing protestors held rival demonstrations yesterday but police in riot gear and dog handlers were forced to intervene when bricks and smoke bombs were thrown.
The local Kent police said in a statement that one person had suffered a broken arm and five others suffered "minor injuries".
Three men were arrested -- one on suspicion of possessing an offensive weapon, a second for allegedly breaching the peace and a third suspected of a public order offence.
More than a million migrants and refugees, many from Syria, crossed into Europe last year, causing the continent's worst migration crisis since World War II.
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Britain has opted out of European Union quotas for taking migrants but has said it will take 20,000 refugees from camps on Syria's borders by 2020.
Earlier yesterday, a further six men were arrested at a motorway service station in Maidstone, northwest of Dover, for alleged violent disorder in an incident which police think was linked to the protests.
Anindya Battacharyya, who was travelling with an anti-fascist group to Dover, told the Guardian newspaper he was inside the service station when violence broke out.
"The service station staff bolted the doors and through the windows we could see a large group of fascists," he said.
"They attacked one of our coaches and smashed up the windows and one of them came and daubed a swastika in blood on the side of one of the coaches."
In total, over 20 weapons were seized in Dover and at the service station including a knuckle duster, hammers and bricks, police said.