Steinmeier said in an interview with German weekly Der Spiegel that "if it cannot be done otherwise, things will be resolved through the appropriate legal channels", adding that "Europe is a community of law".
The German minister spoke specifically of Slovakia and Hungary, which have both made their own threats of legal action against the controversial quota system.
Slovakia said last month that it would complain against the EU quota plan to distribute 160,000 refugees and migrants across the bloc.
"European solidarity is not a one-way street," Steinmeier said, adding that "those who refuse (to welcome refugees) must know what is at stake for them: open borders in Europe".
Europe's Schengen passport-free area is cherished as one of its most important achievements and the European Commission has repeatedly expressed concern that re-imposing border controls threatens its future.
EU leaders on Thursday set an end-of-June deadline to agree on a new border and coastguard force to slow the influx of migrants across the 28-nation bloc's porous external frontiers.
Following a slew of emergency summits this year, they acknowledged they had been too slow to carry out a joint strategy to tackle Europe's worst refugee crisis since World War II.
