Police locked down a section of the city centre as about 2,000 people gathered. Most of those arrested, all men, were suspected of public order offences. Several people suffered minor injuries in sporadic scuffles.
"The presence of so many protesters in the city has proved a challenge and while many have turned out to protest peacefully, the police reaction has been necessary in order to prevent the few hell-bent on violent confrontation," Assistant Chief Constable Garry Shewan said in a statement.
A group called the English Defence League, which says it opposes militant Islam, squared off against a larger group of counter- demonstrators from the group Unite Against Fascism.
Manchester, 200 miles (320 kilometres) northwest of London, is the latest English city to be hit with tensions.
Troubles also have occurred in Luton, Birmingham and London in the last few months involving a loose collection of far-right groups, including the little known English Defence League.The league rejects the fascist label, arguing that it only opposes militant Islam. But several of its supporters made Nazi salutes during Saturday's protest.