Unite Against Fascism Scotland said about 400 protestors turned out for a rally to counter a "White Pride" event in Hunters Square and on the Royal Mile, attended by about 40 people.
Police Scotland said three of the arrests related to religiously-aggravated offences, with the others for minor public order offences.
A spokesman said the protests "on the whole passed off peacefully".
Ten people have been arrested after a fascist demonstration in Edinburgh.