The National Immigration Institute did not say what the supposed FBI investigation was about.
The agency said a total of five Iranians were detained along with their Haitian driver, who was apparently acting as their guide on a highway between the Baja California border cities of Tijuana and Tecate on Wednesday.
It said their car was stopped at a toll booth because agents suspected they were going to try to cross into the United States.
The agency said two of the Iranians were "under observation by the Federal Bureau of Investigations."
The FBI did not immediately confirm the information.