His remarks in an interview with newspaper Bild are likely to further inflame relations between the two Nato allies after Mr Erdogan urged German Turks to boycott Germany's main parties in next month's general election.
"It is clear that in this state, Turkey will never become a member of the EU," Mr Gabriel said.
"It's not because we don't want them but because the Turkish government and Erdogan are moving fast away from everything that Europe stands for."
EU leaders have been critical of Mr Erdogan's crackdown on opponents before and after a failed military coup against him in July last year.
Accession talks have ground to a virtual halt though Turkey remains a candidate for membership.
Turkey's Western allies fear that sweeping new powers Mr Erdogan won in a tightly fought referendum in April are pushing Turkey away from democratic values.
Mr Erdogan says both the crackdown and the increased presidential powers are needed to help tackle serious challenges to Turkey's security both at home and beyond its borders.
At a highpoint in tensions earlier this year, Mr Erdogan angered Germany, home to three million Turks, about half of whom can vote in the election on 24 September, by accusing German authorities of Nazi-like behaviour.
Relations between the two countries have also been strained by Turkey's arrest of a Turkish-German journalist and a German human rights activist.
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