Bishop Heinrich Bedford-Strohm claims it would prevent young Muslims being radicalised and involve them in the local community.
The man who heads up the Evangelical Lutheran Church said "extensive" teaching of Islam would allow Muslims to examine their own religion and avoid fundamentalism.
Speaking to the Heilbronner Stimme newspaper he said: "Tolerance, religious freedom and freedom of conscience must apply to all religions."
At the moment some schools in Germany teach Islam but the classes are not compulsory and can be dropped if the student chooses.
Bishop Bedford-Strohm said students of all faith should be made to learn about Islam after a study found two-thirds of Germans did not believe it had a place in their country.
Germany has recently opened its doors to hundreds of thousands of mainly Muslim refugees fleeing war in the Middle East.