Many Bundesliga fans, angry with the newly-approved tighter security rules in and around stadiums that they say are spoiling the experience, have protested by staying silent for the opening 12 minutes of dozens of games in recent weeks.
"We know that protests are planned among some fans for the game against Hanover," Dortmund said in a letter signed by captain Sebastian Kehl, coach Juergen Klopp, sports director Michael Zorc and chief executive Hans-Joachim Watzke.
"But we also know that many fans will be supporting us. We ask you not to allow trenches to be dug within the fan community and between you and us.
"We have accepted and respected your fears and concerns that triggered the protests in recent weeks. It was not easy playing football in these conditions."
Dortmund, who also defended their Bundesliga title last season, have an average attendance of 80,000 which is the second highest in Europe behind Barcelona.
"So we want to ask you, BVB fans, to support us again tomorrow. Loud. Unconditionally. Patient. Just like we know you. Even for 120 minutes if needed," the letter added.
The German football league and the 36 clubs from the top two divisions voted last week in favour of tougher stadium checks, an increased crackdown as well as sanctions for flares and smoke bombs, video monitoring, and better-trained security staff.
German football is struggling to contain growing fan violence.
A report last month said the 2011-12 season had the highest number of criminal proceedings in 12 years, almost double the amount of injured fans and a more than 20 percent rise in police work hours from the previous season.