Bayern routed Schalke 8-0 last Friday behind closed doors at the Allianz Arena - the highest score for an opening game of a Bundesliga season.
European champions Bayern drew particular criticism in the German media after club officials including chairman Karl-Heinz Rummenigge, president Herbert Hainer and board member Oliver Kahn sat together in the VIP stand.
The DFB criticised "members of the Munich and Schalke delegations" for breaching the hygiene concept by sitting less than 1.50m apart and failing to wear face masks.
Rummenigge has apologised and said Bayern will "do better" for Thursday's UEFA Super Cup showdown against Sevilla in Budapest.
The DFB also warned Eintracht Frankfurt after two players brought their children into a part of the stadium only supposed to be used by the squad after Saturday's 1-1 draw with Arminia Bielefeld.
The German FA has said they will clamp down on Bayern, Schalke and Frankfurt if there is any recurrence.