An Avon and Somerset Police spokeswoman said: "I can confirm three men were arrested for violent disorder following an incident in St Nicholas Street on October 12 and released on police bail pending further inquiries."
City have fined the players two weeks' wages each, and given them a final warning.
A club statement said: "All three have been released on bail pending further police inquiries, but the club has sufficient information to know that there has been a serious breach of its disciplinary code.
"The players concerned have therefore each been fined two weeks' wages and will be given a final warning as to their future conduct."
Defender Partridge is a Wales international, but was suspended for Wednesday night's 2-0 win over Azerbaijan in Cardiff.
Manager Gary Johnson, said: "I will deal with any breach of club discipline with a heavy hand, as any lack of professionalism has to be addressed.
"Heavy fines have been imposed as a result of the incident this week and I have left all the players in no doubt that there must be no repeat.
"It has obviously had a major effect on the preparation for the three players concerned for the Tranmere game and I don't consider them to be in the right frame of mind to be considered for selection."
City chief executive Colin Sexstone added: "The fines imposed are the maximum we can apply, which is an indication of how seriously we view the issue and of our determination to ensure there are no future problems of this nature."
No further details on the alleged incident or where it happened have been released by either the club or the police.