Education Minister Annette Schavan is also in favour of the plan, which was created in response to a ruling by Germany's Constitutional Court.
The country's highest court declared in February that the method by which calculations were made for the children of people on Hartz IV unemployment benefits were unconstitutional.
Schavan, who, like von der Leyen, belongs to the Christian Democratic Union (CDU), told the Welt am Sonntag newspaper that the vouchers would create better education opportunities for children.
But Bavarian Social Affairs Minister Christine Haderthauer, who belongs to the CDU's sister party the Christian Social Union, called the vouchers "discriminatory," and said that they represented a "collective vote of no-confidence towards the long-term unemployed."
Haderthauer also questioned the efficacy of the vouchers, and said that "problem families" would not suddenly start sending their children to music lessons simply because they had a voucher. "They'll just disappear in some drawer," she said.
The German Association of Cities, an organization that represents the interests of towns in social policy issues, has defended the idea. "In order to secure social participation, and to help children more specifically, we should not simply rely on money payouts," organization boss Stephan Articus said.
Articus added, "It would be worthwhile to research whether the state can secure the basic needs of children using chip-cards and vouchers." A chip-card scheme is currently being tested in Stuttgart.