A member of the online forum of the notorious website, 4chan, is believed to have made the threat in response to the actress's speech on gender equality at the UN headquarters in New York at the weekend.
The 24-year-old described her own sexualisation as a teen and her hope for women to be treated equally to men, and for men to support the women in their lives, during her speech on the new HeForShe initiative.
Following her appearance, the anonymous user has created a website, emmayouarenext.com, which displays a countdown to the moment they claim the hacked photos will be revealed in the next few days.
One comment that appeared on the 4chan message board warned: "She makes stupid feminist speeches at UN, and now her nudes will be online."
The post has since been deleted.
The user who claims to have the naked photographs is thought to be the same person behind the recent release of private snaps of Jennifer Lawrence and Kate Upton.
Earlier this month, Emma spoke out about the publication of nude photos of the 'Hunger Games' actress, describing it as a 'violation'.
“Even worse than seeing women's privacy violated on social media is reading the accompanying comments that show such a lack of empathy,” she tweeted.