The FBI said it was investigating “the person or groups responsible for a series of computer intrusions involving high-profile figures”.
Hacked photos of Justin Timberlake and his Friends With Benefits co-star Mila Kunis have also appeared online, according to reports.
Laura Eimiller, of the FBI’s Los Angeles office, said dozens of stars had been the victims of hackers who had stolen personal information from email and other accounts.
She did not name any alleged victims “due to the pending nature of our investigation”.
Reports say that Johansson has contacted the FBI over the leak of the private photos.
It is also reported that her lawyer has sent letters to websites stating that Johansson owns the copyright to the pictures and threatening legal action if they are not removed.
The Johansson photos are gold on the internet. Despite playing a number of sexy roles, she does not usually do nude movie scenes.