Trouble has flared in the past at derby games between the fierce rivals - dozens of fans were arrested when Blackburn won at Turf Moor in the Premier League in March 2010.
And ahead of this weekend's Championship meeting - again at Turf Moor - both clubs have promised a "zero tolerance" reaction to any disorder.
The joint-statement read: "We encourage all supporters attending this game to respect each other and the authorities.
"An East Lancashire derby between our two historic clubs is always a special occasion and we hope Saturday's Championship game will be remembered for the action on the pitch and the positive backing of both sets of supporters.
"We acknowledge that there will be some disruption to the normal matchday schedule.
"However, this has been done with the safety of all supporters in mind and all fans should be aware that breaches of stadium regulations - including anti social behaviour - will not be tolerated.
"Burnley and Blackburn Rovers also have a zero tolerance for discrimination of any sort, on the pitch or in the stands.
"If you experience any form of discrimination before, during or after the game, or require assistance in any matter, please contact a matchday steward. We look forward to welcoming you to Turf Moor."