Money Laundering Crimes Act - Amends the Federal criminal code to establish money laundering as a Federal criminal offense. Sets forth fines and penalties to be imposed against anyone who conducts transactions involving monetary instruments through a financial institution engaged in or affecting interstate commerce: (1) with the intention of carrying out specified types of unlawful activity; or (2) with knowledge that such monetary instruments represent income derived from such unlawful activity. Requires investigation of such an offense by the Federal Bureau of Investigation, the Drug Enforcement Administration, and the Internal Revenue Service, as appropriate. Establishes extraterritorial jurisdiction over such prohibited conduct.