Reinhard Grindel said on Monday on Twitter that "football and the DFB stand for values that Mr. Erdogan doesn't sufficiently observe".
Arsenal's Ozil and Manchester City midfielder Gundogan, who are both German internationals born in Gelsenkirchen and of Turkish origin, met Erdogan in London on Sunday alongside Everton striker Cenk Tosun.
Investors hammered Turkey's lira on Tuesday, sending it to a record low after President Tayyip Erdogan said he plans to take greater control of the economy after next month's election, deepening concerns about his influence on monetary policy. That's why it's not good that our global players let themselves be manipulated for his electoral campaign.
"The thoughts expressed by the DFB president are absolutely unacceptable", Demiroren said in a TFF statement.
Mr Erdogan has been widely criticised for abandoning the secular principles of the state in Turkey.
The meeting comes as Erdogan campaigns for re-election after calling a snap poll for June 24, bringing the vote forward by a year and a half.
Gundogan, in a statement, said he, Ozil and Everton's Cenk Tosun, a Turkey worldwide, attended an event of the Turken Foundation, which assists Turkish students in the United States and the United Kingdom, and met Erdogan there. Footballers of any nationality will always be welcomed by our president, especially when they are the ones who want to have such a meeting. "For its part, the Turkish Football Federation in no way will participate in such behaviour and will continue to comply with the rules set out by UEFA until the last moment of the UEFA EURO 2024 voting".
With the Premier League season now all done and dusted, football fans are now switching their focus to this summer's World Cup in Russian Federation.
"I don't think we should involve them, they are Turkish but are playing for another national team".
The holders even have some new faces this time around in the likes of Leroy Sane and Timo Werner, but two players who look certain to feature have caused a bit of a stir with the German FA.
"Such actions will increase tensions and insecurity in the world", Ali Larijani said, adding that they would not go "unanswered". "It will be a lesson for them".