One person was also treated for a head injury after trouble flared near Sinclair's Oyster Bar on Shambles Square at around 3.30pm.
Football supporters had been gathering in the city centre ahead of Manchester City's Champions League game against Sevilla at the Etihad Stadium
Footage and photographs circulated on social media showing chairs being thrown
Trouble also seemed to have spread to nearby Exchange Square.
A tweet from Greater Manchester Police revealed the three people arrested were Polish
The tweet read: "3 x Polish Football fans arrested for a violent disorder following the incident at Shambles Square earlier this evening."
A statement added: "Three men have been arrested following a fight on Exchange Square.
"Shortly before 3.30pm on Wednesday 21 October, 2015, police received a report of a fight on Exchange Square involving a group of football fans.
"Officers quickly attended the scene and the group dispersed.
"Three men were arrested on suspicion of violent disorder
They have been taken into police custody.
"A man was treated at the scene by paramedics for a head injury.
"Police officers remain on patrol in the city centre this evening."
The trouble is not believed to be linked to the City-Sevilla match.
There were suggestions some of the people involved were wearing the colours of Polish club Slask Vroclaw, whose fans have clashed with those of Sevilla previously.
Source : PA
Source: PA