Schäuble also voiced his opposition to the burqa, the face-covering full-body garment worn by women in some Muslim communities.
The burqa is "exactly the opposite of what we believe communication is about," Schäuble said. "Open societies mean living and talking together and not being separated from each other. And to that extent the burqa is an element that hinders communication."
"We are in favor of not having the burqa," he added. "We want the Muslim community to be well and at ease in the European Union," he stressed, "but also accept the structures and legal setup in Europe."
His comments, to a group of Brussels-based journalists, came days after Germany assumed the rotating EU presidency and as he prepared to host an informal meeting of EU justice and interior ministers in Dresden next week.
"There are still parts of the Muslim world where historical enlightenment still needs to be implemented," he said. "We all know what terrible centuries there were in Europe before the Enlightenment," he added.
He advocated training imams, saying that "imams should contribute to integration."
"This may be a way to make a contribution to ensuring that given the whole diverse aspect of Islam we strengthen those who can live with the European rule of law, universal rights and the achievements of the Enlightenment," he said.
Following in Straw's footsteps
While saying that the question of headscarves was a personal one, he took up a similar position to former British foreign secretary Jack Straw against the burqa -- who outraged British Muslims last year by telling the BBC that he would prefer that Muslim women not wear the nikab, or face veil.
More than three million Muslims live in Germany, and Schäuble said that now 20 percent of the German population had a "migratory background."
Schäuble stressed the need to increase dialogue with Muslims within the EU and admitted that there were still some "deficits" regarding integration in Germany.
"We understand that Islam is part of Germany with equal rights," said the minister. "But that also means they need to accept the fundamental rights and obligations of our society."
"Anyone who cannot accept the equality of men and women has not even come close to meeting one of the basic conditions for the 21st century," he insisted.
In Europe in general "we do need to improve integration as a whole but we need to prevent parallel societies from emerging," he added.