Scottish referendum: Police separate rival groups in Glasgow
The trouble began when the Union supporters fired a flare and charged into George Square.
The square had hosted a pro-independence party ahead of Thursday's independence referendum.
BBC Scotland reporter Cameron Buttle, who was at the scene, said Friday evening's confrontation started quickly with flares being fired and a "co-ordinated" charge from the Unionist side, who were singing Rule Britannia.
Some of the pro-Union side were carrying banners featuring Loyalist imagery.
A spokeswoman for Police Scotland said there were about 100 people in each of the two groups, and although there had been some "minor disorder" it had been dealt with by officers.
She said investigations were under way, with officers conducting inquiries which could lead to further arrests.
There have been reports on social media of a "Yes" supporter being stabbed in George Square, but police said they had no record of any incident.
The square was closed to traffic with local diversions in place.
A number of people draped in union jacks later left the area and began spreading on to the nearby streets, with many marching down St Vincent Place as police followed.
Roads around the square were closed as police dealt with the incident.
A large group of Union supporters later gathered in George Square again, this time at the top of the square next to Queen Street Station.
They sang Rule Britannia and a flare was let off.
Police formed a human barrier to block off the route to Buchanan Street - where scuffles also broke out - and contain people in the square.
After 21:00 the crowd scattered but smaller groups remained along with the line of police officers.
Mounted officers also remained at the scene.