The Avengers Assemble actress claimed to feel "absolutely violated" by Christopher Chaney, who pleaded guilty in March to illegally accessing her emails and those of celebrities including Mila Kunis and Christina Aguilera.
In pre-sentencing papers, prosecutors recommended Chaney pay a little over $66,000 to Johansson and another $7,500 (£4,800) to Aguilera.
The hacker, who claimed shortly after his arrest last October that he is addicted to spying on celebrities, is expected to spend 71 months in federal prison after admitting to nine felony counts, including wiretapping and unauthorised access to a computer.
He will be sentenced on July 23, according to the Los Angeles Times.
Johansson has claimed that the photos circulated by Chaney were meant for her ex-husband Ryan Reynolds.