Rainer Maria Woelki also refuted the Alternative for Germany (AfD) party's claim Islam was incompatible with the country's constitution.
The Cardinal Archbishop of Cologne said mosques are equally protected under Germany's constitution as chapels, adding "whoever says 'yes' to church towers must also say 'yes' to minarets".
He comments come after deputy leader of AfD, Beatrix von Storch, reportedly told the Frankfurter Allgemeine newspaper: "Islam is in itself a political ideology that is not compatible with the constitution.
"We are in favour of a ban on minarets, on muezzins and a ban on full veils."
Refering to Germany as a country with a "painful history", Rainer Maria Woelki said: "Never again must people in this country be marginalized or persecuted for their race, ethnicity or religion."
A right-wing and Euro-skeptic party, AfD has become increasingly popular, particularly since the refugee and migration crisis.