Kick-off at the SchucoArena on October 28 last year was delayed slightly after a flare was thrown onto the pitch from the away supporters' section.
Hertha fans also set off numerous flares towards the end of the match, which finished 0-0 after extra-time before third-tier outfit Arminia won on penalties.
And, citing the "unsportsmanlike conduct" of the fans responsible, the DFB announced on Thursday that Bundesliga club Hertha have been penalised to the tune of €20,000.
The capital club have 24 hours to appeal the ruling.
Hertha resume their campaign following the mid-season break at struggling Werder Bremen on February 1.
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