The 2-2 draw in Duesseldorf that saw second division Fortuna win promotion with a 4-3 aggregate victory that sent Hertha into the second division, was interrupted twice for a total of about 30 minutes by a pitch invasion and flares.
"Our committee has already launched an investigation," the DFB said in a joint statement with the German football league. "We saw the events in this game with consternation and worry."
"The DFB and the league agree that such irresponsible behaviour that threatens the health of many peaceful fans cannot be tolerated and must be punished. The (DFB's) sports court... must find the appropriate punishment."
Hertha, whose players were reluctant to return to the pitch after a 20-minute break with a minute left in stoppage time, have also decided to lodge an appeal.
"We need to play this game until the end. This had nothing to do with a sports event," said Hertha manager Michael Preetz, saying his players had returned to the pitch purely for security reasons so as not to further escalate the situation.
"A normal game was no longer possible for us. The players were afraid," he told reporters on Wednesday, explaining why the club had decided to appeal.
The game was first stopped after Fortuna scored on the hour to take a 2-1 lead, leaving Hertha needing two goals.
Dozens of lit flares from both groups of fans landed on the pitch prompting referee Wolfgang Stark to stop play.
The game was interrupted again for more than 20 minutes deep in stoppage time after hundreds of Fortuna fans poured on to the pitch thinking it was over and forcing both teams to seek refuge in the changing rooms.
It was only after Stark insisted that Hertha's players returned to finish the match that they returned to the pitch to play the remaining 90 seconds of added time.