"We should complement the coalition against terror with a coalition for education," Ursula von der Leyen told a Gulf security conference.
She said members of the US-led coalition fighting the jihadists needed to counter the "brutal lies" of IS with a message of hope for a better future.
"Google, Facebook, YouTube, Instagram and many more platforms have been weaponised," she told the Manama Dialogue.
"People without prospects are easily led to believe such false promises and such brutal lies.
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French Defence Minister Jean-Yves Le Drian echoed the theme in an address to the same forum.
He too said the jihadists could not be defeated by military means alone as they fed off poverty and underdevelopment.
France has carried out air strikes against IS in both Iraq and Syria and has military advisers on the ground.
Germany has provided weapons and training to Kurdish peshmerga fighters taking part in the campaign against IS in northern Iraq.