German minister of the interior Thomas De Maiziere has said football fans who attack police or stewards "should be locked up."
De Maiziere, 63, made the remarks after a season marred by several outbreaks of violence both inside and outside grounds.
On Monday, Eintracht Braunschweig supporters invaded the pitch after their team failed to win promotion to the Bundesliga in a playoff against Wolfsburg.
The following day, 1860 Munich fans threw seats onto the pitch at the Allianz Arena as their team went down to the third tier.
The incidents have led to debate about how to react to the outbreaks of trouble and prevent them from happening again.
And in an interview with football magazine kicker, De Maiziere called for prison terms for perpetrators of violence.
"The outbreaks of violence are unacceptable," he said. "Attacks on players and fans of opposing teams, employees at the stadiums, have nothing to with a sporting competition.
"Whoever attacks stewards or police in truth is no football fan and does not belong in a stadium but rather in prison."
He said he hoped to see "a fast and severe reaction of the judiciary so that everyone knows what to expect if he behaves like that," accusing those involved in violence of "damaging all of football."
Speaking to kicker, former Bayern Munich sporting executive Matthias Sammer blamed "a total decline in values such as respect, civility, honesty and loyalty," while former coaching legend Jupp Heynckes called for a concerted effort to fight what he said was a "social ill."
Meanwhile, German FA (DFB) president Reinhard Grindel said "radical parts" of the Eintracht Frankfurt and Borussia Dortmund support at the DFB Pokal final had "arranged in advance to disturb the cup final massively."
Sections of the crowd jeered a half-time performance by singer Helene Fischer, chanted anti-DFB slogans and set off pyrotechnics.
The DFB has opened investigations against both clubs, who have in the past been punished with partial stadium closures for fan misbehaviour.