The source, 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.
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.
The arrest was connected with "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.
Celebrities and people in the news have long been targets of privacy invasion but concerns have redoubled in the Internet age. In Britain, publisher Rupert Murdoch closed down the News of the World this year after contentions that the tabloid routinely hacked into people's phones in the hunt for exclusive stories.
The paper, which had published for 168 years, faced allegations of systematically intercepting private voicemail of those in the news - including a teenage murder victim.