German fans wanting to watch their side in the tournament in France must first be members of the official fan club before purchasing tickets, hiking up their cost by an additional 40 euros (£32).
The DFB's decision to combine the sales with membership that has a 10 euro sign-up cost and a 30 euro annual fee angered fans of the 2014 World Cup winners.
"Acquiring Euro 2016 tickets is already difficult for football fans as not everyone requesting a ticket gets one," cartel office president Andreas Mundt said in a statement on Tuesday.
"If you couple the possibility of acquiring a ticket with paid fan club membership then not only is the price is increased but in case of not being awarded a ticket one still has to pay the membership fee."
The investigation is the latest to plague the DFB, which is struggling with the fallout from a scandal involving the 2006 World Cup in Germany and several ongoing probes resulting from it.
Germany have been drawn in Group C along with Ukraine, Northern Ireland and Poland in the tournament in France starting on June 10.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
