The images were apparently taken by Johansson on her smartphone camera, the BBC says, and the incident follows the leaking of photos of other stars including Jessica Alba and Vanessa Hudgens.
One leaked photo appears to show Johansson, 26, topless on a bed while another apparently shows her wearing a towel while revealing her naked backside in a mirror.
"The FBI is aware of the alleged hacking incident and is looking into it," an FBI official told FoxNews.com.
Laura Eimiller, of the FBI's office in Los Angeles, said dozens of Hollywood celebrities had been the victims of hackers who had stolen personal information from email and other internet accounts, Agence France-Presse reports. However, Eimiller did not name other alleged victims.
There are also reports of a hacked photo of Justin Timberlake taken by actress Mila Kunis.
The FBI said it is investigating "the person or groups responsible for a series of computer intrusions involving high-profile figures," the BBC reports.
Celebrity gossip website TMZ.com says Scarlett Johansson's lawyer has sent letters to websites saying that Johansson owns copyright of the photos, and threatening legal action if they are not taken down.