Two men, aged 35 and 49, were detained for breach of the peace while a 23-year-old woman was arrested for obstructing police officers.
The incident happened at about 14:00 in Buchanan Street, while a pro-refugee rally was taking place in the same area.
A spokesman from Police Scotland: "All three people were later released."
He added: "A report will be prepared for the procurator fiscal."
Three people have been arrested following a disturbance near a demonstration in Glasgow city centre.