Police Scotland said the arrests included a large group of people who left Glasgow Green and engaged in further disorder in the city centre.
A statement released on Saturday evening said a number of containments were put in place, including on Oswald Street.
The arrests related to offences including assault, possession of offensive weapons, breach of the peace, obstruction and resisting arrest.
Ch Supt Emma Croft said: “We have seen significant disorder from disparate groups in Glasgow today at what should have been peaceful, lawful protests.
“Incidents of this nature can understandably cause a great deal of concern, and our officers took quick and decisive action to protect the public and bring the situation to conclusion.
“I want to be clear that the behaviour from many of these groups is not legitimate protest, it amounts to violence, intimidation and fear and will not be tolerated.”
She said officers had recovered weapons that indicated there an intention for pre-meditated disorder, violence, and intimidation.
Croft continued: “This is completely unacceptable behaviour and those involved should be in no doubt that they will be identified and held to account for their actions.
“At a time when Glasgow should be shown at its best, it is extremely disappointing to once again be dealing with violence and disorder that attempts to create unease in our communities.”
“The protests and associated incidents have now concluded. We will continue to have a visible policing presence in the city centre and surrounding areas.”
