Germany international team-mates Ozil and Gundogan, who are of Turkish descent, had their picture taken with the country's President Recep Tayyip Erdogan in London on Sunday.
While a seemingly innocuous occurrence, DFB chiefs Reinhard Grindel says the association have taken issue with the pair appearing in the photos one month ahead of the 2018 World Cup finals, given Erdogan's increasingly authoritarian stance in recent years.
"The DFB, of course, respects the special situation for our players with migrant backgrounds, but football and the DFB stands for values that Mr. Erdogan does not sufficiently respect," Grindel said, as quoted by ESPN.
"Therefore, it is not a good thing that our internationals have let themselves be exploited for his election campaign stunt. It certainly hasn't helped the DFB's integration efforts."
Germany team coordinator Oliver Bierhoff also expressed concern over the photos and said he would speak with the players.
"I still have absolutely no doubts about Mesut and Ilkay's commitment to playing for the Germany national team and how much they identify with our values. They were unaware of the symbolism of these pictures, but we cannot endorse it, and we will discuss the matter with the players."