Around 1,000 people in total turned out for the demonstrations.
It began in City Square and outside the Park Plaza, with the a party in support of former English Defence League leader Tommy Robinson setting off along Boar Lane after 1pm
The counter-protest, run by the Anti-Fascist Network, headed to Vicar Lane.
Police on foot and on horses then prevented each group, gathered outside both ends of Kirkgate Market, from meeting.
The originally-planned march then turned back down Boar Lane and on to Briggate at around 2pm.
A major policing operation was conducted.
West Yorkshire Police were supported by the mounted section and additional police officers from other forces, along with support from partner agencies.
There was around 40 minutes of serious disruption to traffic and residents on Vicar Lane but no serious disorder, officers said.
One Special Constable was taken to hospital who required medical treatment after being hit by a bottle.
There were three arrests, one for theft, obstructing a police officer and public order and a small number of Section 35 (Dispersal) notices given to protesters.
It is believed there was a total of nearly 1,000 people took part in the planned protests, around 250 people from the first group and 750-counter protesters.
The demonstrations in Leeds came to a close at around 4pm.
A protest of around 23 people also took place at the Bullring in Wakefield.
It lasted for around half an hour and finished before 1.30pm.
Around 90 counter protestors also held a demonstration at Wakefield Cathedral.
No arrests were made at the event.
Chief Superintendent Mabs Hussain, who was the commander of the operation, said: “I would like to pass on my gratitude to all officers and staff, partnership agencies, residents and visitors to Leeds and Wakefield, for their conduct and co-operation during the demonstrations this afternoon, which did cause some disruption for a short period of time.
“One of our special constables, who volunteered to work today, was injured during the demonstrations in Leeds.
"This is completely unacceptable and the incident is currently being investigated.
“We ensured we had appropriate resources including assistance from our mounted section and additional high visibility police officers, to minimize the disruption caused as much as possible.”