The Federal Bureau of Investigation is conducting a criminal investigation of a Florida company accused of scamming millions from customers during the period that Matthew Whitaker, the acting U.S. attorney general, served as a paid advisory-board member, according to an alleged victim who was contacted by the FBI and other people familiar with the matter.

The investigation is being handled by the Miami office of the FBI and by the U.S. Postal Inspection Service, according to an email sent to the alleged victim last year by...