Missiles were thrown and police vehicles damaged during a disturbance at a Tommy Robinson campaign event.
The former English Defence League leader, real name Stephen Yaxley-Lennon, was due to appear in Oldham.
Footage posted on social media showed clashes between his supporters and counter-demonstrators in Limeside.
Greater Manchester Police said “objects including eggs and bricks” were thrown and there was damage to two police vehicles.
The force said there were no reported injuries and rumours someone had been stabbed were false.
It is unclear where Mr Robinson – who is campaigning for the European elections as a candidate for north-west England – was during the trouble.
Jim McMahon, Labour MP for Oldham West and Royton, tweeted: “It’s horrible to see our town being used for hate and division when our own future is a shared one, long after the circus has left town.
“Very different from our own stall in Oldham earlier today where we celebrated our town.”
Police said they understood that many of the people involved were not from Oldham and appealed for anyone with information to come forward.
Ch Supt Neil Evans added: “Police officers responded quickly to the disorder and dispersed those involved. Fortunately, no-one was seriously hurt and damage was only caused to vehicles.
“Those involved can expect to be arrested and dealt with robustly.”
Mr Robinson is running as an independent to become an MEP for north-west England, one of 11 candidates in the constituency.