Charlotte Knobloch, the new president of the council, said: "It is urgently necessary to rearrange history lessons as the topic of National Socialism is not given enough space."
She said many teachers leading the subject did not know enough about the period, and that this is not helping to curb the rise of neo-Nazi sentiments, particularly in the east of the country.
"In the new federal states (former East Germany) there are still teachers who know nothing about the past," she said.
"In Saxony, the horror is almost a reality today. Neo-Nazi sentiments should not be fed and the way to combat the extremism is through education.
"The topic of National Socialism could be its own school subject. And it must be regulated so that it is carried out in schools across the country."
But her history proposals have been received with scepticism by the Culture Ministers' Conference, the association of education ministers from each of Germany's states.
Ute Erdsiek-Rave, president of the conference and minister for education in Schleswig-Holstein, said: "The Holocaust is also dealt with in other subjects, such as German, politics and social studies, ethics and religious education.
"It is questionable whether a separate subject on National Socialism can encompass all of these things. "National Socialism and the Holocaust are fixed components in the training given to teachers and no pupil leaves school without some knowledge of this chapter of German history."
Ms Knobloch has also called for Islam lessons in schools to tackle extremism among Muslims.
She said: "If you control what Muslim children learn, then the danger that they become indoctrinated by extremists is reduced."