One person was arrested out of state, Los Angeles FBI spokeswoman Laura Eimiller said. She declined to release further details before an 11 a.m. PDT press conference.
However, the person familiar with the investigation, who requested anonymity because the details had not yet been announced, told The Associated Press that a Florida man has been indicted on charges that he hacked into the email accounts of celebrities, including Johansson.
A call to a representative for Johansson was not immediately returned.
The arrested involved Operation Hackerazzi, a year-long FBI investigation of computer hacking that targeted Hollywood celebrities, Eimiller said.
Nude shots of Johansson appeared on an Internet site earlier this year and TMZ.com reported that hackers stole them from her cellphone.