The 13 were arrested by police for offences of public order and violence during the protest which was attended by fewer than 1,000 EDL supporters.
Some threw bottles, cans, stones and three smoke bombs at opponents gathered nearby.
Nearly 100 supporters of the far-right group climbed over a temporary 8ft barricade - aimed at keeping them inside the city's Urban Gardens - to get on to neighbouring waste ground from where they threw missiles at police.
As the skirmishes were breaking out, nearly 300 people gathered for an alternative event hosted by Unite Against Fascism/We Are Bradford about half a mile away at the Crown Court Plaza.
A West Yorkshire Police spokeswoman said of the 13 arrests, eight were from Bradford and the others from Wakefield, Leeds, Wolverhampton, Walsall and Birmingham.
In the days before the rally, Bradford community leaders called for calm fearing demonstrations could provoke a violent reaction to rival the 2001 Bradford riots, where 191 people were given sentences totalling more than 510 years.
Initially the EDL intended to march in Bradford with a planned protest by Unite Against Fascism on the same day.
A high-profile campaign was started to stop the EDL march and a 10,000-signature petition opposing it was handed to the Home Office.
Home Secretary Theresa May was asked to authorise the ban by Bradford Council.
It came after West Yorkshire Police's Chief Constable, Sir Norman Bettison, wrote to the council requesting an order to prohibit any public processions over the August Bank Holiday weekend.
In a joint statement police and the Bradford Council praised local people for remaining calm during a difficult day when tensions could have risen.
Ch Supt Alison Rose, Bradford South divisional commander, and council leader Ian Greenwood said: "Although there has been some disruption to the city centre, we are returning to normality and people of Bradford are now able to continue their lives.
"The police has worked effectively to handle the situation and to respond quickly to the events as they unfolded.
"The mood of the city in general has been one of calm and local people have co-operated and supported the police by behaving sensibly or staying away.
"We have done a lot of work with the local community in the build-up to these events and we would like to thank those who helped to plan for and managed the protests.
"The numbers of English Defence League supporters in Bradford were less than they claimed.
"Unite Against Fascism has also had a similar presence in the city."
The EDL supporters met in Halifax before travelling to Bradford on buses under police escort for the static demonstration.
Members had travelled from many towns and cities across England, including Hull, Merseyside, Manchester, Stoke, Southport, Dudley, Wigan and Stockport.
Only one entrance to the gardens was open and protesters had to pass through metal detectors to gain entry.
One EDL supporter, a Muslim called Abdul Salaam, 40, from Glasgow, was escorted into the gardens by police under a chorus of shouting from opponents.
Unravelling a Glasgow Rangers flag, he asked reporters: "Why are they against the United Kingdom?
"Islam doesn't teach you hatred, it teaches you peace. These people are hypocrites, they are not true Muslims."
Another EDL member said: "It's not about being white and proud, it's about being English and proud."
When trouble flared, police pushed the EDL members away from the edge of the barricade towards the centre of the gardens, while their opponents were moved into neighbouring streets.
Then the far-right group held a rally as police in riot gear held their line.
Skirmishes broke out between EDL supporters and their own stewards, who stood in front of the police.
Ashiq Hussain, chair of We Are Bradford, said: "Today we had a peaceful, united, multicultural event attended by Christian, Muslim, Jewish, Sikh, Hindu communities, trade unions and anti-fascists.
"We said we would organise a peaceful celebration and that is what we did."
Sabby Dhalu, joint secretary of Unite Against Fascism, added: "All those that wanted to peacefully voice opposition to the EDL today have been vindicated.
"The EDL have once again exposed itself as a fascist, violent and criminal conspiracy against Britain's Muslims and other communities.
"Allowing the EDL to come to Bradford, while telling those that oppose them to stay at home is wrong.
"The EDL's sole intention of coming to Bradford was to cause violence and mayhem.
"Trouble did occur in Bradford only at the hands of the EDL, not because of events opposing them.
"The majority of British people abhor the EDL and the fascism, racism, Islamophobia and hatred they peddle, and will always turn up to oppose the EDL, as they did in Bradford today.
"That is why it is crucial to have organised and peaceful events opposing them and this is precisely what we achieved today.
"We are the majority; the EDL is a tiny minority. We have the right and freedom to peacefully voice our opposition to the EDL and other fascist organisations."