The law was passed in a 128-62 vote in the lower chamber of parliament, was prompted by FIFA bribery scandals in recent years.
Switzerland-based sports leaders such as FIFA President Sepp Blatter and IOC President Thomas Bach are now classed as "politically exposed persons" in wider legislation covering money-laundering.
Swiss lawmaker Roland Buechel says "normally these rules are for politicians and dictators."
Buechel says the law also applies to executive committee members and employees of sports federations.
The law allows greater scrutiny of "any strange movement" in bank accounts and financial assets held in Switzerland, Buechel says.