Seven people were arrested by Avon and Somerset Police last week after trouble between fans in Cardiff last October.
South Wales Police are investigating an assault on a steward and serious disorder which occurred at the game.
Both forces said they would crack down on anyone "causing problems before, during or after the game".
Insp Rob Millican, from Avon and Somerset Police, said it would "not tolerate disorder".
"We have arrested a number of Bristol City fans and will now put these people before the courts," he said.
"Successful convictions should result in football banning orders which will mean they will no longer be able to attend games or follow their national side abroad.
"We urge all attending this weekend's match to enjoy themselves but we will not tolerate poor behaviour."
Fans have been warned anyone carrying, lighting or throwing such items as flares or smoke bombs will be arrested and could be prosecuted.
Saturday's Championship game between Bristol City and Cardiff City, kicks off at 12:00 GMT.
Bristol and Cardiff City fans have been warned to behave at Saturday's Severnside derby following a previous clash between the clubs.