Violence broke out before the Cup game on October 31, which Hannover won 4-3 on penalties following a 1-1 draw after extra-time, as 300 Dynamo fans broke into Hannover's AWD Arena and clashed with police, which held the match up for 15 minutes.
"The weight of the punishment is explained by the numerous precedents and the seriousness of the incidents at the Cup game in Hanover," explained Hans Lorenz, president of the German Football Federation's (DFB) disciplinary panel after a seven hour hearing late Monday.
Last year the DFB fined the eastern German side €100,000 after rioting at Dortmund.
In the last 20 years, the DFB's disciplinary committee has returned 20 verdicts against Dresden with a wide range of sanctions and fines.
Monday's sanction comes 48 hours before Germany's first and second division clubs meet in Frankfurt to discuss controversial new measures to curb crowd trouble.
Last month German fans reacted against the proposals which will see a ban on standing and a cut in ticket availability by staging silent protests at stadiums across the country.