Dramatic video footage showed dozens of officers charging down Hope Street to head of a counter protest that had formed close to the main march, which involves controversial Republican group Cairde Na hEireann.
The group's Twitter announced earlier: "Today Cairde na hÉireann will march to La Pasionaria statue on the Clydeside to remember the 550 people from Scotland who fought in the International Brigades, 65 of them losing their lives, against Franco’s fascist forces in the Spanish civil war."
They later tweeted: "A huge thanks to everyone that took part in today's commemoration in Glasgow. It was great to see Irish republicans turn out in numbers to remember the International Brigades. We will never bow down to threats and intimidation from fascists in our city. ¡No Pasaran!"
A second march went from Blythswood Square to Barrowlands Park, where leaders gave speeches.
Counter-protesters were hemmed in by police at the former Old Ship Bank pub near Trongate.
Police confirmed that over 1000 people took part in the march and counter demonstration, and condemned the use of pyrotechnics which injured an officer.
Assistant Chief Constable Bernard Higgins, said: “We had significant resources deployed throughout Glasgow city centre as these public processions took place.
“The majority of those who took part in the processions listened to us and complied with our instructions. A significant number of those who attended as part of the counter protests were intent on stopping the processions from taking place but were prevented from doing so by prompt and decisive police action.
“I am, however, disgusted at the recklessness and stupidity of those who decided to throw pyrotechnics, one of which injured an officer.
“He was simply carrying out a duty which allows us to facilitate people's rights and ultimately we were here today to keep everybody safe.
“We take the welfare of our officers very seriously and will be supporting him and his colleagues as he recovers and will continue in our work to trace those responsible.
“I utterly condemn any acts of violence and would like to thank officers and staff whose dedication and professionalism helped us successfully deliver a first-class policing operation on what was a very challenging day.”
The demonstration comes just a week after ugly scenes in Govan last Friday evening, which saw clashes between loyalists opposed to a separate march in favour of Irish unity.
Two men have since been arrested in connection with the incident.
Today's marches were allowed to go ahead by Glagow City Council despite concerns that more violent clashes could take place.