Steinmeier said that "fair play" was a "value that extends far beyond the world of sport", in comments made in the Portuguese capital Lisbon and released by his foreign ministry in Berlin.
"Corruption poisons politics and it poisons sport. If football is meant to serve as a model then this must be cleared up," Steinmeier said.
"If the football world does not manage to cleanse itself of this, then government agencies have to step in," Steinmeier added.
World football's governing body FIFA is grappling with a vast corruption scandal after seven football officials were detained by Swiss police at the request of United States authorities as part of a suspected corruption case involving more than $150 million in bribes.
Swiss investigators have also raided FIFA's headquarters as part of an investigation into the awarding of the 2018 and 2022 World Cups to Russia and Qatar.