Officers said they were aware of claims that a woman had been assaulted during a “heated debate” between the two sides on Argyle Street but were still to establish the facts.
On Saturday night a spokesman for Police Scotland said: “Around 40 Yes and No campaigners were involved in a heated debate on Argyle Street at approximately 4pm on Saturday. An allegation was made that during the demonstration a woman was assaulted, this has not yet been confirmed.
“Investigations are ongoing and a male has been detained.”
According to an eye witness the alleged assault took place after the women tried to grab a megaphone from one of two men.