The 19-year-old, who lives in the London area, is accused of making the post on social media during the inquiry to find the 13-year-old.
The man was arrested by the Metropolitan Police and is currently in custody.
Rumours and gossip had plagued the internet since the youngster went missing from her Mansfield home on the evening of Saturday, 30th May.
Her body was found in a hedgerow off Westfield Lane - less than a mile from her home - three days later.
She was found hanged, and police have repeatedly emphasised there are no suspicious circumstances.
Despite this, there were still some taking to Facebook and spreading wild accusations.