Hundreds of men waving Union flags sang Rule Britannia and God Save the Queen as police contained them in a "loose kettle".
The men could also be heard chanting: "You can stick your independence up your a***" and "If you hate Alex Salmond clap your hands".
Many of the men, who were mostly aged between 20 and 40, appeared to be quite intoxicated. One boasted that "Glasgow would burn for voting Yes", adding that it was now "payback time".
A large number of the demonstrators attempted to move onto nearby Cochrane Street but were prevented by the heavy police presence.
Police in Glasgow were forced to send in mounted officers to control the crowds. Photo / AP
As the situation deteriorated, demonstrators tried to gain access to the city's main train station, which was promptly closed by police.
It is understood that some of the demonstrators were members of the far-right Scottish Defence League and English Defence League. Flags and banners associated with Glasgow Rangers were also spotted in the crowd.
A video posted on the Twitter account Referendum Boys appeared to back up these claims.
https://twitter.com/referendumboys
Earlier, one middle-aged woman wearing a Yes badge attempted to make her way through George Square during the demonstration when she was accosted by a group of men in their 20s. The men spat at the clearly shocked woman and called her "scum".
Some protesters also shouted "scum" at police officers attempting to maintain order.
Also witnesses claimed they saw glass bottles thrown by demonstrators as tensions in the city escalated.
Union supporters and people sporting Yes badges argued over the referendum result and a chorus of Rule Britannia was countered by the Scottish anthem, Flower of Scotland.
Roads around the square were closed as police dealt with the incident.
Witnesses claim that one drunken man boasted that "Glasgow would burn for voting Yes". Photo / AP
After 9pm the crowd scattered but smaller groups remained and the line of police officers stayed.
Mounted officers also remained at the scene.
A spokeswoman for Police Scotland said investigations were under way which could lead to more arrests.
She said: "Three people have been arrested so far in relation to the incident in George Square. Retrospective inquiries will be carried out which may lead to further arrests."
Earlier, Assistant Chief Constable Bernard Higgins asked the public to remain calm following the referendum result.
He said: "It is to everyone's credit that they remained calm on a day of potentially high emotion and co-operated fully with our Police Officers and also the staff at Polling Places on a day when record numbers turned out to vote.
"This meant the ballot and count passed off smoothly and there were just a very few isolated incidents across the country involving a small number of alleged offences."
He continued: "Police Scotland had plans in place to ensure the safety and security of the Referendum and these worked.
"I would also like to thank our Police Officers across the country for the hard work and effort they put in to ensure the day went well."
Mr Higgins confirmed that over the period of the referendum ballot and count there were six arrests across the country mainly for alleged breaches of the peace and assaults.
"As we move forward the public can be assured Police Scotland is committed to keeping people safe. We will respond appropriately and proportionately to any issues which may arise."
