U.S. federal prosecutors have launched a criminal investigation into whether individuals at Mossack Fonseca & Co., the law firm at the center of the “Panama Papers” scandal, knowingly helped its clients launder money or evade taxes, according to people familiar with the matter.

Mossack Fonseca has been in the global spotlight since early April, when a consortium of journalists published a trove of leaked documents showing that the Panama-based law firm created hundreds of thousands of shell companies and offshore accounts...