Amber, 13, went missing from her Mansfield home on Saturday evening and her body was found on Tuesday evening.
A Facebook post, which claimed it was not worth searching for her because she had been murdered, was seen at about this time, officers confirmed.
Police have confirmed Amber's death is not being treated as suspicious.
A spokesman said: "We are aware of an offensive Facebook post which was seen yesterday evening by many people supporting our efforts to find missing Amber Peat.
"We would like to let the public know we are robustly investigating and will work hard to bring to justice anyone who publishes such appalling posts to social media."
The force declined to confirm the exact wording of the post, but it is believed to have carried graphic details of a violent attack.
Amber went missing after what her parents described as a minor row about chores.
Hundreds of people volunteered to help with the search and posters were put in shops, house windows and on lamp posts.
Her body was found in a small patch of woodland, close to roads and housing, by a dog walker.
The cause of death has been confirmed as hanging.
A social media post that falsely claimed missing Nottinghamshire schoolgirl Amber Peat had been murdered is being investigated by police.