The awarding of the 2018 FIFA World Cup to Russia forms part of one of the two corruption investigations launched on Wednesday.
"Without going into the details of the accusations ... this is clearly another case of illegal exterritorial use of US law," a statement on the website of the Russian foreign ministry read.
"We hope that this will not in any way be used to cast a shadow on the international football organisation as a whole and its decisions.
"Once again we are calling on Washington to stop attempts to make justice far beyond its borders using its legal norms and to follow the generally accepted international legal procedures."
Swiss police detained several FIFA leaders in a dawn raid as part of a twin corruption inquiry that rocked world football's governing body two days before its leader Sepp Blatter seeks a new term.
No Russians are among the seven people detained on suspicion of paying bribes and kick-backs over the past two decades.
The investigation plans to question 10 members of the FIFA executive committee who took part in the 2010 vote awarding the World Cups to Russia for 2018 and Qatar for 2022.
The committee since 2009 includes Russia's Sports Minister Vitaly Mutko, though it is not clear whether he is one of the people to be questioned.
Mutko told Tass news agency that he has "nothing to hide" and is ready to provide any information.
